Surface Areas of Prisms, Cylinders, - Kyrene School District · 2014. 4. 14. · 9-4 Surface Area...
Transcript of Surface Areas of Prisms, Cylinders, - Kyrene School District · 2014. 4. 14. · 9-4 Surface Area...
9-4 Surface Areas of Prisms, Cylinders,
and Spheres
Course 2
Warm Up
Problem of the Day
Lesson Presentation
Warm Up Find the volume of each figure to the nearest tenth. Use 3.14 for . 1. rectangular pyramid 7 ft by 8 ft by 10 ft tall
186.7 ft3
12.6 ft3
33.5 ft3
162 ft3
2. cone with radius 2 ft and height 3 ft
3. sphere with diameter 4 ft
4. triangular pyramid with base 54 ft2 and height 9 ft
Course 2
9-4 Surface Area of Prisms, Cylinders, and
Spheres
Problem of the Day
When my age is divided by 2, 3, 4, or 6 there is always a remainder of 1, but when it is divided by 7 there is no remainder. How old am I?
49
Course 2
9-4 Surface Area of Prisms, Cylinders, and
Spheres
Learn to find the surface area of prisms,
cylinders, and spheres.
Course 2
9-4 Surface Area of Prisms, Cylinders, and
Spheres
Vocabulary
net
surface area
Insert Lesson Title Here
Course 2
9-4 Surface Area of Prisms, Cylinders, and
Spheres
If you remove the surface from a three-dimensional figure and lay it out flat, the pattern you make is called a net. You can construct nets to cover almost any geometric solid.
Course 2
9-4 Surface Area of Prisms, Cylinders, and
Spheres
SURFACE AREA OF A POLYHEDRON
The surface area of a polyhedron is found by adding the areas of each face of the polyhedron.
Since nets allow you to see all the surfaces of a solid at one time, you can use them to help you find the surface area of a three-dimensional figure. Surface area is the sum of the areas of all surfaces of a figure.
Course 2
9-4 Surface Area of Prisms, Cylinders, and
Spheres
You can use nets to write formulas for the surface area of prisms. The surface area S is the sum of the areas of the faces of the prism. For the rectangular prism shown,
S = lw + lh + wh + lw + lh + wh
= 2lw + 2lh + 2wh Top
Bottom
Front Back
Left Right w
h
l
Course 2
9-4 Surface Area of Prisms, Cylinders, and
Spheres
Find the surface area of the prism formed by the net.
Additional Example 1: Finding the Surface Area of a
Prism
= 2lw + 2lh + 2wh S
= (2 · 15 · 9) + (2 · 15 · 7) + (2 · 9 · 7) S Substitute.
S = 270 + 210 + 126
S = 606
The surface area of the prism is 606 in2.
Multiply.
Add.
Course 2
9-4 Surface Area of Prisms, Cylinders, and
Spheres
Find the surface area of the prism formed by the net.
= 2lw + 2lh + 2wh S
= (2 · 4 · 6) + (2 · 4 · 3) + (2 · 6 · 3) S Substitute.
S = 48 + 24 + 36
S = 108
The surface area of the prism is 108 in2.
Multiply.
Add.
Try This: Example 1
4 in.
6 in.
3 in. 3 in.
Course 2
9-4 Surface Area of Prisms, Cylinders, and
Spheres
4 in.
If you could remove the lateral surface from a cylinder, like peeling a label from a can, you would see that it has the shape of a rectangle when flattened out.
You can draw a net for a cylinder by drawing the circular bases (like the ends of a can) and the rectangular lateral surface as shown below. The length of the rectangle is the circumference, 2r, of the cylinder. So the area of the lateral surface is 2r. The area of each base is r2.
r Circumference of cylinder (2r)
h
Course 2
9-4 Surface Area of Prisms, Cylinders, and
Spheres
SURFACE AREA OF A CYLINDER
The surface area S of a cylinder is the sum of the areas of its bases, 2r2, plus the area of its lateral surface, 2rh.
S= 2r2 + 2rh
Course 2
9-4 Surface Area of Prisms, Cylinders, and
Spheres
Find the surface area of the cylinder formed by the net to the nearest tenth. Use 3.14 for .
Additional Example 2: Finding the Surface Area of a
Cylinder
6 ft
6 ft
8.3 ft
S = 2r2 + 2rh
S (2 · 3.14 · 62) + (2 · 3.14 · 6 · 8.3) Substitute.
Use the formula.
S 226.08 + 312.744
S 538.824
S 538.8
The surface area of the cylinder is about 538.8 ft2.
Multiply.
Add.
Round.
Course 2
9-4 Surface Area of Prisms, Cylinders, and
Spheres
Find the surface area of the cylinder formed by the net to the nearest tenth. Use 3.14 for .
9 ft
9 ft
20 ft
S = 2r2 + 2rh
S (2 · 3.14 · 92) + (2 · 3.14 · 9 · 20) Substitute.
Use the formula.
S 508.68 + 1130.4
S 1,639.08
S 1,639.1
The surface area of the cylinder is about 1,639.1 ft2.
Multiply.
Add.
Round.
Try This: Example 2
Course 2
9-4 Surface Area of Prisms, Cylinders, and
Spheres
Unlike the surface of a prism or a cylinder, the surface of a sphere cannot be flattened without stretching or shrinking.
Course 2
9-4 Surface Area of Prisms, Cylinders, and
Spheres
Because the surface of a sphere cannot be flattened out, it is impossible to make a net for a sphere. However, there is an exact formula for the area of a sphere.
SURFACE AREA OF A SPHERE
The surface area S of a sphere is 4 times times the radius r squared.
S= 4r2
Course 2
9-4 Surface Area of Prisms, Cylinders, and
Spheres
Find the surface area of the sphere to the nearest tenth. Use 3.14 for .
Additional Example 3: Finding the Surface Area of a
Sphere
S = 4r2
S 4 · 3.14 · 82
S 803.84
S 803.8
The surface area of the sphere is about 803.8 m2.
Use the formula.
Substitute.
Multiply.
Round.
Course 2
9-4 Surface Area of Prisms, Cylinders, and
Spheres
Find the surface area of the sphere to the nearest tenth. Use 3.14 for .
S = 4r2
S 4 · 3.14 · 62
S 452.16
S 452.2
The surface area of the sphere is about 452.2 in2.
Use the formula.
Substitute.
Multiply.
Round.
Try This: Example 3
6 in.
Course 2
9-4 Surface Area of Prisms, Cylinders, and
Spheres
Lesson Quiz
Find the surface area of each figure to the nearest tenth.
3. a sphere with radius 6 ft
100.5 ft2 352.0 ft2
Insert Lesson Title Here
452.2 ft2
2,317.3 in2
4. A drum is closed on the top and the bottom. The diameter of the drum is 18 in. The height is 32 in. Find the surface area.
1. 2.
Course 2
9-4 Surface Area of Prisms, Cylinders, and
Spheres