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Create Representations to Communicate Mathematical Ideas (1)(E) Use a net to find the total surface area of each prism.

1. 2. 3.

4. a. Classify the prism at the right.

b. Find the lateral area of the prism.

c. The bases are regular hexagons. Find the sum of their areas.

d. Find the total surface area of the prism.

Use formulas to find the total surface area of each prism. Round your answer to the nearest whole number.

5. 6. 7.

Find the lateral area of each cylinder to the nearest whole number.

8. 9.

Find the total surface area of each cylinder in terms of P.

10. 11.

19 cm6.5 cm

29 cm

6 ft

6 ft

6 ft

4 in.

4 in.8 in.

4 cm10 cm

10 ft5 ft

4 ft

5 in.8 in.

4 in.

Regularoctagon

5 cm

22 cm

4 in.

6 in.12 9 m6 m

8 cm

2 cm 7 in.

11 in.

continuedProblem 4

The area covered is the lateral area of a cylinder with height 6 in. and diameter 2.5 in.

L.A. = pdh Use the formula for lateral area of a cylinder.

= p(2.5)(6) Substitute 2.5 for d and 6 for h.

= 15p ≈ 47.1 Simplify.

In one full turn, the stencil roller covers about 47.1 in.2.

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20. Apply Mathematics (1)(A) Some cylinders have wrappers with a spiral seam. Peeled off, the wrapper has the shape of a parallelogram. The wrapper for a biscuit container has base 7.5 in. and height 6 in.

a. Find the radius and height of the container.

b. Find the total surface area of the container.

21. Analyze Mathematical Relationships (1)(F) Suppose you double the radius of a right cylinder.

a. How does that affect the lateral area?

b. How does that affect the total surface area?

c. Use the formula for surface area of a right cylinder to explain why the total surface area in part (b) was not doubled.

22. Apply Mathematics (1)(A) A cylindrical can of cocoa has the dimensions shown at the right. What is the approximate surface area available for the label? Round to the nearest square inch.

What is the surface area of each solid in terms of P?

23. 24.

7.5 in.

6 in.

STEM

7 in.

5 in.

8 cm

7 cm

4 cm10 in.

3 in.

8 in.

TEXAS Test Practice

25. The height of a cylinder is twice the radius of the base. The total surface area of the cylinder is 56p ft2. What is the diameter of the base to the nearest tenth of a foot?

26. Two sides of a triangle measure 11 ft and 23 ft. What is the smallest possible whole number length, in feet, for the third side?

27. A polyhedron has one hexagonal face and six triangular faces. How many vertices does the polyhedron have?

28. The shortest shadow cast by a tree is 8 m long. The height of the tree is 20 m. To the nearest degree, what is the angle of elevation of the sun when the shortest shadow is cast?

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Find the lateral area of each three-dimensional figure to the nearest whole number.

1. 2. 3.

Find the total surface area of each pyramid to the nearest whole number. For the cone, find the total surface area in terms of P.

4. 5. 6.

7. Justify Mathematical Arguments (1)(G) Explain why the altitude PT in the pyramid at the right must be shorter than all of the lateral edges PA, PB, PC, and PD.

8. Create Representations to Communicate Mathematical Ideas (1)(E) Draw a square pyramid with a lateral area of 48 cm2. Label its dimensions. Then find its total surface area.

9. The lateral area of a cone is 4.8p in.2. The radius is 1.2 in. Find the slant height.

10. Connect Mathematical Ideas (1)(F) The lateral area of a pyramid with a square base is 240 ft2. Its base edges are 12 ft long. Find the height of the pyramid.

Find the total surface area of each composite figure to the nearest whole number.

11. 12. 13.

14. Apply Mathematics (1)(A) The roof of a tower in a castle is shaped like a cone. The height of the roof is 30 ft and the radius of the base is 15 ft. What is the lateral area of the roof? Round your answer to the nearest tenth.

15. Explain Mathematical Ideas (1)(G) Suppose you could climb to the top of the Great Pyramid. Which route would be shorter, a route along a lateral edge or a route along the slant height of a side? Which of these routes is steeper? Explain your answers.

4.5 m

4 m

6 m

4 m4 m

3 cm

4 cm

7.2 in.

8 in. 6 ft

8 ft

2 V3 m4 m

8 m

D

P

A

T

BR

C

4 m

4 m

3 m

3 m

6 ft

5 ft

12 ft

2 m2 m

4 m

2 m

STEM

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Find the volume of each cone in terms of P and also rounded as indicated.

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Find the volume to the nearest whole number.

9. � 10. 11.

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13. Apply Mathematics (1)(A)� 5IF�1ZSBNJE�PG�1FBDF�BOE�"DDPSE�JT�BO�PQFSB�IPVTF�JO�"TUBOB �,B[BLITUBO��5IF�IFJHIU�PG�UIF�QZSBNJE�JT�BQQSPYJNBUFMZ����N�BOE�POF�TJEF�PG�JUT�TRVBSF�CBTF�JT�BQQSPYJNBUFMZ����N�

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14. Apply Mathematics (1)(A)� #VJMEFST�VTF�B�QMVNC�CPC�UP�GJOE�B�WFSUJDBM�MJOF��5IF�QMVNC�CPC�TIPXOűBU�UIF�SJHIU�DPNCJOFT�B�SFHVMBS�IFYBHPOBM�QSJTN�XJUI�B�QZSBNJE��'JOE�JUTűWPMVNF�UP�UIF�OFBSFTU�DVCJD�DFOUJNFUFS�

15. Analyze Mathematical Relationships (1)(F)� "�DPOF�XJUI�SBEJVT���GU�BOE�IFJHIU����GU�IBT�B�WPMVNF�PG���p�GU3��8IBU�JT�UIF�WPMVNF�PG�UIF�DPOF�GPSNFE�XIFO�UIF�GPMMPXJOH�IBQQFOT�UP�UIF�PSJHJOBM�DPOF

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4 ft

4 ft 4 in.

5 in.12

3 m

2 m

7.5 in.

7 in.Square base

12 cm

15 cm

Equilateral base

24 ft

15 ft

24 ft

Square base

9 ft

STEM

STEM

6 cm

3 cm

2 cm

588 Lesson 14-5 Volumes of Pyramids and Cones

TEXAS Test Practice

35. What is the diameter of a sphere whose surface area is 100p m2?

A. 5 m B. 10 m C. 5p m D. 25p m

36. Which of the following statements contradict each other?

I. Opposite sides of ▱ABCD are parallel.

II. Diagonals of ▱ABCD are perpendicular.

III. ▱ABCD is not a rhombus.

F. I and II G. II and III H. I and III J. none

37. What is the reflection image of (3, 7) across the line y = 4?

A. (3, 3) B. (-7, 3) C. (3, 1) D. (3, -7)

Find the volume in terms of p of each sphere with the given surface area.

24. 25p yd2 25. 144p cm2 26. 49p m2 27. 225p mi2

28. Apply Mathematics (1)(A) An ice cream vendor presses a sphere of frozen yogurt into a cone, as shown at the right. If the yogurt melts into the cone, will the cone overflow? Explain.

29. The surface area of a sphere is 5541.77 ft2. What is its volume to the nearest tenth?

30. Apply Mathematics (1)(A) The circumference of Earth at the equator is approximately 40,075 km. About 71% of Earth is covered by oceans and other bodies of water. To the nearest thousand square kilometers, how much of Earth’s surface is land?

Find the surface area and volume of each figure. Leave your answer in terms of P.

31. 32.

33. What is the lateral surface area of a sphere with radius 2 in.?

A. 11p B. 2p C. 8p

D. There is no lateral surface area of a sphere.

34. You are constructing a model of the planet Mercury. Which of the following measures cannot be used to describe the model?

A. volume C. circumference

B. lateral surface area D. weight

12 cm

4 cm

4 cm

4 cm

4 cm2.5 cm

2 cm

2.5 cm

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