Lesson 1C ~ Area of Triangles and Parallelograms Name__________________________________________ Period______ Date____________ Find the area of each figure. 1. 2. 3. Perimeter = 44 cm

©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

Plot each set of points and find the area of each figure. 4. (2, 6), (–2, –1) and (7, –1) 5. (–7, –2), (–4, 5), (3, –2) and (6, 5)

Area: __________ Area: __________

Solve for x. 6. Area = 35 cm² 7. A = 58.9 in² 8. A = 36 m² 9. Sketch and label three different triangles that have an area equal to 60 square feet. 10.

The area of the shaded triangle is 15 cm². The base of the parallelogram is 14 centimeters long. Find the area of the parallelogram.

7.4 m

12.5 m

436 ft

9 21 ft

x

20 cm

x

x x

6.2 in

8 cm

Lesson 2C ~ Area of a Trapezoid Name__________________________________________ Period______ Date____________ Calculate the area of each trapezoid. 1. 2. 3. b1 = 14 feet 6.8 cm

b 2 = 24.5 feet h = 6.5 feet

10.5 cm

4.1 cm

11.3 m

16.4 m

7 m

Find the unknown base or height of each trapezoid. 4. Area = 120 ft² 5. A = 68 cm² 6. A = 31.35 m²

©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

8 ft

18 ft

2b 6 cm

10 cm

h 3.1 m 5.5 m

1b

7. A brick is shaped like a trapezoid. The area of the brick is 25 square inches. The top of the brick is 8 inches. The bottom of the brick is 12 inches. How tall is the brick? 8. A trapezoidal placemat is 32 cm tall. The bottom of the placemat is 48.5 cm. The total area of the placemat is 1419.2 square centimeters. How long is the top of the placemat? 9. Sketch and label 2 trapezoids that have equal areas. 10. Sketch and label 3 different trapezoids that each have an area of 70 square inches. One trapezoid should have whole number measurements. The next trapezoid should have decimal measurements. The third set of measurements should all be fractions.

Lesson 3C ~ Parts of a Circle Name__________________________________________ Period______ Date____________ Draw each part inside the circle provided.

1. Radius AB. 2. Diameter CD . 3. Chord EF . 4. Central ∠GHI 5. Sketch a diagram of B with the following parts:

a. chord JK b. radius AB c. diameter PQ

6. Sketch a diagram of a circle with central angle JWR, a radius with an endpoint labeled H, and a diameter HY. Use tools (compass, ruler and protractor) to accurately draw each circle on a separate sheet of paper. 7. M with a 3 cm radius. How long will the diameter be?

8. K with a diameter that is 4 inches long. How long is the radius?

9. H with the following parts: radius HA of 8 cm, diameter CD , central angle MHG with a measure of 65° and chord XY that is 10 cm.

10. A circle with a radius of 6 cm, the longest chord TR and a central angle PBJ which equals 130°.

Find the missing measure of each unknown central angle.

11. 12. 13.

x°

151° y° x°

y° y°

x°y°

©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

14. Sketch a circle divided into three central angles: ( ) ( ) ( )°+°−°+ 23 and 42,8 xxx . Solve for x then find the measure of each angle.

y° 115° x° 65°

©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

Lesson 4C ~ Circumference and Pi Name__________________________________________ Period______ Date____________ Find each missing measure. Use 3.14 for π. 1. C ≈ 48.67 ft 2. C ≈ 30.772 cm 3. C ≈ 297.044 in diameter = _____ radius = ______ r = ___ and d = ___ Draw a diagram for each exercise. Show work. Use 3.14 for π. 4. A dinner plate fits tightly into a box whose square base has a perimeter of 28 inches. What is the circumference of the plate? 5. The spoke of a bicycle is 1 foot long. How many revolutions will the tire make when it is ridden one mile? (1 mile = 5280 feet) 6. A satellite is 1,500 km above the earth, traveling in a circular orbit. The radius of the earth is close to 6,400 km. How far does the satellite travel in one orbit around the earth? 7. A semicircular swimming pool has a diameter of 24 meters. Find the perimeter of the pool. 8. Describe what happens to the circumference of a circle when the radius is cut in half. Show work to support your answer. 9. On a separate sheet of paper draw and label a circle with a circumference between 6 and 10 inches. Show work to support your answer.

Lesson 5C ~ Area of a Circle Name__________________________________________ Period______ Date____________

Find the missing length(s) in each circle. Use 3.14 for π.

1. Area ≈ 28.26 ft² 2. Area ≈ 314 mi² 3. Area ≈ 113.04 cm²

x mi

x ft

x cm y cm

4. A goat is tied to a post in a grass field. He can graze on 153.86 square feet of grass. How long is the rope? 5. The circumference of a circular swimming pool is 34.54 meters. What is the area of the pool? The area of each circle is given. Find the length of the radius, length of the diameter and the exact circumference.

6. Area = 25π cm² 7. A = π square inches 8. A = 0.49π ft² 9. The circumference of a circle is 12π inches. Find the exact area of the circle. 10. Three students were asked to find the area of the circle at the right.

.14

Describe the errors in the work of each student.

Student 1:

A = πr²

≈(3.14)(14)² ≈ 615.44

Student 2:

A = πr²

≈(3.14)(14) ≈ 87.92

Student 3:

A = πr²

≈(3.14)(7) ≈ 21.98

©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

Lesson 6C ~ More Pi Name__________________________________________ Period______ Date____________

©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

Sketch and label a circle to match each description then shade the indicated sector. 1. A sector measuring 90°. 2. A circle with a 40° sector. 3. A 210° sector. Complete the proportion. Then, find the area of the labeled sector. A represents the area of the entire circle and x represents the area of the sector. 4. A = 35 in² 5. A = 254.34 m² Write a proportion then find the area of the labeled sector. Use 3.14 for π. Round answers to the nearest hundredth. 6. 7. 8. 9. A sprinkler rotates back and forth forming a 164° central angle. The sprinkler can reach plants that are 30 yards away from it. Find the area that can be watered by this sprinkler.

. 35

=x

x = ______

°=

360 x

x = _______

. 5 in 45°

. 9 cm

130°

6 cm

Sector of a circle: part of a circle formed by a central angle and the intercepted arc. Example 1: Find the area of the 50° sector in the circle below. 1. Find the area of the circle, . 6 π2r 04.1132 =π 2. Write a proportion in the form:

°

=360

angle central of Degreecircleof Areasector of Area

°°

=36050

04.113 2cmx

50° 6 cm . 3. Cross multiply. 360 5652=x 4. Solve for x. 15x = 2 7. cm

.135°

. 15 ft 210°

Lesson 7C ~ Complex and Irregular Figures Name__________________________________________ Period______ Date____________

Calculate the area of each shaded region. Use 3.14 for π. 1. 2. 3.

32 ft

25 ft

25 ft

18 ft

18 ft

.

8 cm

5 in

14 in

9 in

©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

4. 5. The area of the shaded region is given. Find each missing measure. 6. Area = 108 in² 7. A = 768 ft² 8. A = 119 cm²

h

12 in 12 in

x ft

32 ft

24 ft

27 ft

8 cm

x cm

8 cm

5 cm

.

. .

.

(–6, –8)

(0, 10)

(6, –8)

(10, 0)

y y

x

(6, 8)

x0, 0)

(0, –10)

(0,

(1

(–6, –8)

(6, –8) (0, –10)

.

. . .

. . . .

10)

(–6, –8)

Lesson 8C ~ Circle Similarity Name__________________________________________ Period______ Date____________ Complete the chart using each ratio comparing two circles.

Scale Factor Radii Diameters Circumference Area Volume

8 : 3

1: 4

5 : 2

2 : 7

16 : 25

8 : 27

1. 2. 3. 4. 5. 6. 7. In the table above, what four ratios in each row are the same? Why? Find the missing measure. Use 3.14 for π when needed. 8. The circumference of M is 47.1 meters. The diameter of H is 8 meters.

a. Find the ratio of their circumferences.

b. Find the ratio of the diameters.

c. What is the ratio of their radii? 9. The radius of a child’s wading pool is 5 feet. The area of an adult swimming pool is 706.5 square feet. Find the ratio of the diameters. 10. The ratio of the areas of two circles is 121 : 64. What is the ratio of their circumferences? 11. A flying disc is packed tightly inside of a box with a square base for shipping. The area of the base of the box is 144 square inches.

a. Find the ratio of the length of the base of the box to the diameter of the circle.

b. What is the ratio of the area of the base of the box to the area of the circle? ©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

Lesson 9C ~ Area of Sectors Name__________________________________________ Period______ Date____________

Use a proportion to find the area of each shaded region. Use 3.14 for π. Round answers to the nearest hundredth.

©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

1. 2. 3. 72°

6 cm 4 cm

45°

d =8.6 m

r =5 ft 130°

Use a proportion and the given information to solve for x. Round to the nearest hundredth, as needed. Use 3.14 for π. 4. Area of sector = 32.4 m² 5. Area of sector = 314 ft² 6. Area of sector = 6.28 cm² Area of circle = x Area of circle = 706.5 ft² Radius of circle = x 7. A slice of pizza is 22.608 in². The diameter of the pizza is 24 inches. How many slices of pizza will there be if each piece has the same central angle measure? 8. A circular patio is divided into 16 equal sectors. The radius of the patio is 14 feet. Find the area of one sector. 9. A sector of a circle measures 35°. The area of the sector is 312.6 cm².

a. Find the area of the circle. Round to the nearest hundredth.

b. Find the length of the radius. Round to the nearest whole number.

c. Find the circumference.

d. How long is the arc of the sector? (An arc is a segment of the circumference of the circle that is contained by a central angle.) Round to the nearest hundredth.

45°

73° x°

x

Lesson 10C ~ Three-Dimensional Figures Name__________________________________________ Period______ Date____________

Name two common, everyday objects for each description.

1. Cylinder 2. Cone

3. Rectangular prism 4. Square prism

5. Sphere 6. Hemisphere (half of a sphere)

7. Square pyramid 8. Octagonal prism Name one solid, if possible, that matches each description. 9. 12 edges 10. 5 vertices 11. 8 faces 12. 6 vertices and 9 edges 13. Zero vertices 14. 6 lateral faces 15. One vertice 16. Two bases 17. 7 edges Complete the chart, using the given information. Choose between cone, pentagonal prism, sphere, square pyramid and triangular prism.

©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

18. 19. 20. 21. 22.

Name of the

solid Number of

Edges Number of

Vertices Number of

faces Number of lateral faces

Number of bases

0

5

15

6

1

Lesson 11C ~ Drawing Solids Name__________________________________________ Period______ Date____________

Sketch and label a net of each solid. 1. 2.

©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

3. 4. A square pyramid with base perimeter of

24 ft and a slant height of 8 ft.

Use the given information to draw each 3-dimensional solid. 5. 5 faces, 6 vertices and 9 edges 6. 2 faces, 0 vertices and 0 edges 7. 6 faces, 6 vertices and 10 edges 8. 6 congruent faces, 12 vertices and 12 edges 9. Determine if each net will fold to make a cube. A star has been placed on the base of each possible cube, if the cube folds correctly. Draw a star in the square that is the top of the cube a. b. c.

14 ft 7 cm

8 ft 4 cm

11 cm

8 in

8 in

in

12 in

8

8 in

8 in

Lesson 12C ~ Surface Area of Prisms Name__________________________________________ Period______ Date____________ The surface area of each prism is given. Find the missing measure. 1. Surface Area = 408 m² 2. SA = 869 in²

10 in

6.6 in

x in

22 in

10 in

4 m x m 6 m

3. The surface area of the hexagonal prism, at right, is 4,900 ft². Each base is 525 ft². The height of the prism is 110 ft.

110 ft a. Find the perimeter of the base.

b. Assuming each side of the base is equal in length, find the length of one side.

4. Sketch and label a rectangular prism with lateral area equal to 70 cm². 5. Sketch and label a triangular prism with surface area equal to 70 cm². 6. Sketch and label 3 different prisms (a rectangular prism, triangular prism and hexagonal prism) that each have surface area equal to 500 square inches. Show work to justify your sketches.

©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

Lesson 13C ~ Surface Area of Cylinders Name__________________________________________ Period______ Date____________ 1. The area of the base of a cylinder is 254.34 square meters. The height of the cylinder is 18.5 meters. Use 3.14 for π.

a. Find the length of the radius.

b. What is the lateral area of the cylinder?

c. Determine the total surface area. 2. The lateral area of a cylinder is 1946.8 in². The cylinder is 25 inches tall. Use 3.14 for π.

a. Find the circumference of the cylinder.

b. What is the length of the radius?

c. Find the total surface area.

The surface area is given. Determine the height of each cylinder. Use 3.14 for π. 3. SA = 755.17 ft² 4. SA = 9894.14 cm² 46

©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

5. A manufacturer of steel pipe paints the inside and outside of each pipe. Each pipe is 3 feet long. The outer radius is 3 inches. The inside radius is 2.75 inches. Determine how many square inches needs to be painted on each pipe. Use 3.14 for π. 6. Sketch a diagram of a prism and a cylinder that have equal surface areas. Show work to support your answer.

x ft

6.5 ft

cm

x cm

Lesson 14C ~ Surface Area of Regular Pyramids Name__________________________________________ Period______ Date____________ Determine if the statement applies to all pyramids, all prisms, both pyramids and prisms or neither. 1. The lateral faces are rectangles. 2. It has two bases. 3. The number of faces is always odd. 4. Always has an even number of edges. 5. The number of faces is always even. 6. All faces are triangles.

Use the given information to find each missing measure. Round answers to the nearest hundredth, as needed. 7. Lateral Area = 210 cm² 8. Surface Area = 86 cm² Area of the base = 13.02 cm²

4.3 cm

4.3 cm 4.3 cm

x cm

4.3 cm 4.3 cm

14 cm x cm x cm 9. A regular hexagonal pyramid has a base with 12.5 inch sides. The lateral area of the pyramid is 701.25 square inches. Find the slant height of the pyramid. 10. Shayla bought her mother an ornament. She wants to wrap it in a square pyramidal gift box. The base of the pyramid is 14 cm on each side. The slant height is also 14 cm. Shayla needs an extra 30% of wrapping paper for overlap. How much total wrapping will Shayla need?

©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

11. Find the surface area of the composite solid at the right.

6 in

6 in

6 in

8 in

Lesson 15C ~ Surface Area of Cones Name__________________________________________ Period______ Date____________ 1. The surface area of an orange safety cone is about 301.25 square inches. The radius of the cone is 4.3 inches. Use 3.14 for π.

a. Find the area of the base of the cone. b. Determine the lateral area of the safety cone. c. Find the slant height of the cone.

Use the given information to find each missing measure. Use 3.14 for π.      2. Lateral area = 244.92 in² 3. Lateral area = 890.19 m² 4. Surface area = 590.32 mm² 6.5 in

27 m

x m

x in

x mm 8.0 mm 5. Rachel’s job is to spray small cones with paint. Each cone has a radius of 3 inches and a slant height of 9 inches. The paint costs $34.50 per gallon. One gallon will cover 3,000 square inches.

a. How many parts can Rachel cover with one gallon of paint?

b. Today she plans to paint 400 cones. How many gallons will she need? Round up to the nearest gallon.

c. The company estimates that they will need to 18% more than what is actually needed, for overspray. What is the cost to spray 400 cones?

d. If Rachel only needs to spray the lateral area of each cone find the cost to paint 400 cones. Include the extra 18% for overspray.

©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

Lesson 16C ~ Surface Area of Composite Solids Name__________________________________________ Period______ Date____________

Find the surface area of each composite solid. When necessary, use 3.14 for π. 1. 2.

©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

      3. A rectangular prism has a cylinder cut out of it. The prism is 5 feet by 7 feet by 12 feet. The cylindrical cut-out has a 4 foot diameter and is 12 feet tall.

a. Sketch a diagram of this compound figure.

b. Determine the total surface area of the figure, including the cutout. Use the given information to find the missing measure. Use 3.14 for π, when needed. 4. SA = 615.44 m² 5. SA = 324.35

x m

9 m

4 m

8 m

1 m

1 m 1 m

1 m

5 m

8 m

8 m

8 m

3.5 cm 4.9 cm

4.9 cm

2 cm

6.5 in

6.5 in

8 in

x in

Lesson 17C ~ Volume of Prisms Name__________________________________________ Period______ Date____________ 1. A block of ice is 40 cubic inches. Sketch and label (with measures) three different prisms that could represent the block of ice. 2. A hexagonal swimming pool has a base area of 110 square meters. The volume of the pool is 192.5 cubic meters. How tall is the swimming pool? Use the given information to find each missing measure. Round to the nearest tenth. 3. Volume = 687.96 cm³ 4. V = 67.5 in³ 5. V = 120 yd³ 1 in

©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

6. Clara has a rectangular fish tank that can hold 24 cubic feet of water.

a. How many cubic inches of water can the fish tank hold?

b. The directions instructed Clara to fill the fish tank up 80% of the way. How many cubic inches of water would this be?

c. Clara bought 8 fish to put in the tank. Each fish represents approximately 1.5 cubic inches of water. Now how much water should Clara put in the take to keep the total volume at 80%?

8.4 cm

x in 4.5 cm

x cm

15 in

x yd

4 yd

12 yd

Lesson 18C ~ Volume of Cylinders Name__________________________________________ Period______ Date____________ Find each missing measure. Use 3.14 for π, if necessary. 1. Volume = 427.04 ft³ 2. V = 266.9 cm³ Height = ________ Radius = ________

x cm 4 ft

x

©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

3.4 cm ft 3. The circumference of a round swimming pool at a resort is 314 feet. Use 3.14 for π.

a. How much ground area will the swimming pool require?

b. City building codes require the owner to allow an extra 5 feet all the way around the pool. How much area will be required for the pool and the required extra space?

c. The pool is 5 feet tall, how much water can it hold?

d. The instructions say that the pool should only be filled to 32 of its capacity. How much

water should be put in the pool?

e. Why would the recommendation be to fill the pool only to 32 of its capacity?

4. A cylindrical glass has a 3-inch diameter and is 7 inches tall. Cierra likes to fill her glass with as much ice as possible. She can fit 12 ice cubes in her glass. Each ice cube is 1.25 inches on each side. How much orange juice can Cierra pour into her glass without it overflowing? Use 3.14 for π. 5. A giant cylindrical ocean aquarium can hold approximately 240,000 gallons of water. One cubic foot is equal to 7.5 gallons. Sketch and label, in feet, a cylindrical tank that can hold approximately 240,000 gallons. Be sure to give the length of the radius and the height of the tank. Use 3.14 for π.

Lesson 19C ~ Volume of a Sector of a Cylinder Name__________________________________________ Period______ Date____________ Find the volume of each sector. Use 3.14 for π. Round answers to the nearest hundredth, as needed. 1. A cylinder has a 90° sector removed from it. The cylinder has a 8-foot radius and is 24 feet tall. Find the volume of the cylinder with the missing sector. 2. A circular cake is cut into 18 pieces. The cake is 2

15 inches tall, with a 14 inch diameter. Find the volume of one slice of cake. 3. A plastic tile line shaped like a tube is used to drain water from a wheat field. The tile line is 250 yards long. The tile has an 8-inch diameter. During the rainy season the tile line will be half full.

a. Find volume of water in the tile line, in cubic feet, during the rainy season.

b. Find volume of water in the tile line, in cubic inches, during the rainy season.

Find each missing measure. Use 3.14 for π. 4. The volume of the sector of the cylinder 5. The volume of the sector of a cylinder, is 9,616.25 cubic meters. Find the height. below, is 175.84 cm³. Find the length of the radius.

©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

6. A flower vase has a base shaped like a semi-circle. The radius of the vase is 4

32 inches. When the vase is filled two-thirds of the way it holds approximately 4

171 in³ of water. How tall is the vase? 7. A circular aquarium tank is divided into 24 equal sectors to keep species of fish separated. The tank is 7 feet tall. The tank is only filled to 4

3 of its height. One sector of the tank holds 134.6275 cubic feet of water. Find the diameter of the aquarium?

17.5 cm

32°

50°

21 m

h

Lesson 20C ~ Volume of Pyramids Name__________________________________________ Period______ Date____________ 1. Sketch a diagram of a square pyramid with a volume of 80 cm³. Then, sketch prism with a congruent base and height to the pyramid and calculate the volume of the prism. Use the given information to find each missing measure. Round answers to the nearest hundredth.

2. Volume = 102 m³ 3. Volume = 85180 ft³ 4. Volume = 688 m³

Pyramid height = _____ Area of the base = 88 m² x m

8.5 m

21 ft8

x m

43 ft 12

x m 5. The perimeter of the base of a regular triangular pyramid is 33 yards. The height of the pyramid is 15 yards. The volume of the pyramid is 261.25 cubic yards. What is the height of the triangular base of the pyramid? 6. A pyramid with a square base has sides that are 5 feet long and a height of 9 feet.

a. How does the volume change when the height is doubled?

b. How does the volume change when the length of each side of the base is doubled?

c. Do these findings stay true for any square pyramid? Explain.

©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

Lesson 21C ~ Volume of Cones Name__________________________________________ Period______ Date____________ Find each missing measure. Use 3.14 for π. Round to the nearest hundredth.

1. Volume = 345 mm³ 2. Volume = 179.5 ft³ 3. V = 54.95 cm³ Area of the base ≈ ____ Height of the cone ≈ ____ Radius ≈ ____

©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

4. A cone has a volume of 6π cubic meters. The height of the cone is 2 meters. What is length of the radius? 5. A snow cone cup is 12 cm tall and has a diameter of 10 cm. Snow cones cost $2.00. Serena only has $1.00. The vendor agrees to give Serena half of the volume of a regular snow cone. What is the volume of Serena’s snow cone? 6. A bucket brigade is used when a fire truck cannot get to a fire. A bucket brigade is a human chain where a bucket is passed from one person to another to extinguish a fire. In one brigade the buckets were shaped like cones with a handle. Each bucket was a cone with a 1 foot diameter and 1.25 feet tall. A rectangular prism that is 8 feet long, 3 feet wide and 2.5 feet tall was filled with water. How many buckets of water did it hold? 7. Mount Saint Helens erupted in 1980. The radius of the base of the mountain is 19,685 feet. Before the eruption the mountain was 9,677 feet tall. After the eruption the mountain is 8363 feet tall. The radius of the crater is 7,392 feet.

a. Find the volume of Mount St. Helens before the eruption.

b. Find the volume of the cone shaped top that exploded during the eruption.

c. What is the volume of Mount St. Helens after the eruption?

7 mm

3.5 ft

h

r

8.4 cm

Lesson 22C ~ Volume of Composite Solids Name__________________________________________ Period______ Date____________ Find the volume of each composite solid. Use 3.14 for π. 1. 2. Find the volume of the solid with the base 26 ft

©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

shown below. The height is 4 feet. 34 ft 3. A machine drills conical holes into a cube. Each cube has sides that are 9 cm. The diameter and height of the cone are 9 cm each. Find the volume of the figure after the hole is drilled. 4. A cylindrical can holds three balls. The balls touch the top, bottom and sides of the can. The radius of one ball is 6 cm. Find the volume of the remaining space inside the cylinder. The formula, 3

34 πrV = , gives the

volume of a sphere. Find each missing measure. Use 3.14 for π. 5. Volume = 1690 m³ 6. Volume = 1028.35 m³ Height of prism = ______ Radius = ______

8.5 ft

12 ft

13.5 ft 25 ft

5 ft 8.5 ft

.

9 m

h 13 m

m

11.6 m

4.5 m

13

Lesson 23C ~ Similar Solids Name__________________________________________ Period______ Date____________ 1. Complete the chart.

©2010 SMC Curriculum Oregon Focus on Surface Area and Volume

2. What must be the relationship between any two figures in order to use the ratio shortcuts? 3. What two ratios will always be the same value, if the figures are similar? 4. Give an example of an occupation that uses these ratio shortcuts. Explain how the ratios might be used. 5. The prisms are similar. The surface area of the small prism is 80 square units. a. Find the surface area of the large prism.

b. Write the ratio, in simplest form, of the surface area of the small prism to the surface area of the large prism. c. Identify the linear ratio. d. Find w. Round to the nearest hundredth.

6. The cylinders are similar. The volume of the large cylinder is 7850 cubic units. a. Find the volume of the small cylinder.

b. Write the ratio, in simplest form, comparing the volume of the large cylinder to the volume of the small cylinder. c. Find h. d. Determine the area of the base of the large cylinder.

w 15

10

22.8

Scale Factor Linear Ratio Area Ratio Volume Ratio

1:1

g:h

121:16

64:27

5

2

h