Download presentation

Published byMatteo Reed Modified over 4 years ago

1
Preview Warm Up California Standards Lesson Presentation

2
Warm Up Identify the figure described. 1. two parallel congruent faces, with the other faces being parallelograms 2. a polyhedron that has a vertex and a face at opposite ends, with the other faces being triangles prism pyramid

3
**AF3. 1 Use variables in expressions describing geometric quantities (e**

AF3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = bh, C = pd–the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively). Also covered: AF3.2 California Standards 1 2

4
Vocabulary surface area net

5
The surface area of a three-dimensional figure is the sum of the areas of its surfaces. To help you see all the surfaces of a three-dimensional figure, you can use a net. A net is an arrangement of two-dimensional figures that can be folded to form a three-dimensional figure.

6
The surface area of a cylinder equals the sum of the area of its bases and the area of its curved surface. To find the area of the curved surface of a cylinder, multiply its height by the circumference of the base. Helpful Hint

7
**Additional Example 1: Finding the Surface Area of a Prism**

Find the surface area S of the prism. A. Method 1: Use a net. Draw a net to help you see each face of the prism. Use the formula A = lw to find the area of each face.

8
**Additional Example 1A Continued**

A: A = 5 2 = 10 B: A = 12 5 = 60 C: A = 12 2 = 24 D: A = 12 5 = 60 E: A = 12 2 = 24 F: A = 5 2 = 10 Add the areas of each face. S = = 188 The surface area is 188 in2.

9
**Additional Example 1: Finding the Surface Area of a Prism**

Find the surface area S of each prism. B. Method 2: Use a three-dimensional drawing. Find the area of the front, top, and side, and multiply each by 2 to include the opposite faces.

10
**Additional Example 1B Continued**

Front: 9 7 = 63 63 2 = 126 Top: 9 5 = 45 45 2 = 90 Side: 7 5 = 35 35 2 = 70 S = = 286 Add the areas of each face. The surface area is 286 cm2.

11
**Additional Example 2: Finding the Surface Area of a Pyramid**

Find the surface area S of the pyramid. S = area of square + 4 (area of triangular face) S = s2 + 4 ( bh) 1 2 __ S = ( 7 8) 1 2 __ Substitute. S = 28 S = S = 161 The surface area is 161 ft2.

12
**Additional Example 3: Finding the Surface Area of a Cylinder**

Find the surface area S of the cylinder. Write your answer in terms of . ft S = area of curved surface + (2 area of each base) S = (h 2r) + (2 r2) Substitute 7 for h and 4 for r. S = (7 2 4) + (2 42) S = (7 2 4)+ (2 16) Simplify the power.

13
**Additional Example 3 Continued**

Find the surface area S of the cylinder. Write in terms of . S = 56 + 32 Multiply. S = ( )p Use the Distributive Property. S = 88p The surface area is about 88p ft2.

14
Check It Out! Example 1 Find the surface area S of each prism. B. Method 2: Use a three-dimensional drawing. top side front 8 cm 10 cm 6 cm Find the area of the front, top, and side, and multiply each by 2 to include the opposite faces.

15
**Check It Out! Example 1B Continued**

top side front 8 cm 10 cm 6 cm Front: 6 = 48 48 2 = 96 Top: 6 = 60 60 2 = 120 Side: 8 = 80 80 2 = 160 S = = 376 Add the areas of each face. The surface area is 376 cm2.

16
**Find the surface area S of the pyramid.**

Check It Out! Example 2 Find the surface area S of the pyramid. 5 ft 10 ft S = area of square + 4 (area of triangular face) S = s2 + 4 ( bh) 1 2 __ S = ( 5 10) 1 2 __ Substitute. 10 ft S = 25 5 ft S = S = 125 The surface area is 125 ft2.

17
**S = area of lateral surface + (2 area of each base)**

Check It Out! Example 3 Find the surface area S of the cylinder. Write your answer in terms of . 6 ft 9 ft S = area of lateral surface + (2 area of each base) S = (h 2r) + (2 r2) Substitute 9 for h and 6 for r. S = (9 2 6) + (2 62) S = (9 2 6) + (2 36) Simplify the power.

18
**Check It Out! Example 3 Continued**

Find the surface area S of the cylinder. Write your answer in terms of . S = 108 + 72 Multiply. S = ( )p Use the Distributive Property. S = 180p The surface area is about 180p ft2.

19
Lesson Quiz Find the surface area of each figure. Use 3.14 as an estimate for . 1. rectangular prism with base length 6 ft, width 5 ft, and height 7 ft 2. cylinder with radius 3 ft and height 7 ft 3. Find the surface area of the figure shown. 214 ft2 ≈188.4 ft2 208 ft2

Similar presentations

© 2019 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google