1. Course 2 Unit 5 Lesson 7 Unit 5 Lesson 7 Properties of Volume and Surface Area Properties of Volume and Surface Area

2. Learn to find the volume and surface area of similar three-dimensional figures.

3. Recall that similar figures are proportional. The surface areas of similar three-dimensional figures are also proportional. To see this relationship, you can compare the areas of corresponding faces of similar rectangular prisms.

4. Area of front of smaller prism Area of front of larger prism 3 · 5 6 · 10 15 (3 · 2) · (5 · 2) (3 · 5) · (2 · 2) 15 · 2 2 Each dimension has a scale factor of 2. You can multiply the numbers in any order. So (3 · 2) · (5 · 2) is the same as (3 · 5) · (2 · 2). Remember!

5. The area of the front face of the larger prism is 2 2 times the area of the front face of the smaller prism. This is true for all of the corresponding faces. Thus it is also true for the entire surface area of the prisms. SURFACE AREA OF SIMILAR FIGURES The surface area of a three-dimensional figure A is equal to the surface area of a similar figure B times the square of the scale factor of figure A. surface area of figure A surface area of figure B (scale factor of figure A) 2 =

6. The surface area of a box is 35 in 2. What is the surface area of a larger, similarly shaped box that has a scale factor of 7? Finding the Surface Area of a Similar Figure S = 35 · 7 2 Use the surface area of the smaller box and the square of the scale factor. S = 35 · 49Evaluate the power. S = 1,715 Multiply. The surface area of the larger box is 1,715 in 2.

7. The surface area of a box is 1,300 in 2. Find the surface area of a smaller, similarly shaped box that has a scale factor of Finding the Surface Area of a Similar Figure Course 2 1212. S = 1,300 · 1212 2 1414 S = 325 The surface area of the smaller box is 325 in 2. Use the surface area of the original box and the square of the scale factor. Evaluate the power. Multiply.

8. Insert Lesson Title Here Course 2 The surface area of a box is 50 in 2. What is the surface area of a larger, similarly shaped box that has a scale factor of 3?

9. Course 2 1313. The surface area of a box is 1,800 in 2. Find the surface area of a smaller, similarly shaped box that has a scale factor of

10. Course 2 1313. S = 1,800 · 1313 2 1919 S = 200 The surface area of the smaller box is 200 in 2. Use the surface area of the original box and the square of the scale factor. Evaluate the power. Multiply. The surface area of a box is 1,800 in 2. Find the surface area of a smaller, similarly shaped box that has a scale factor of

11. Given the scale factor, find the surface area of the similar prism. 1. The scale factor of the larger of two similar triangular prisms is 8. The surface area of the smaller prism is 18 ft 2. Insert Lesson Title Here Course 2

12. Given the scale factor, find the surface area of the similar prism. 2. The scale factor of the smaller of two similar triangular prisms is. Insert Lesson Title Here Course 2 1313 The surface area of the larger prism is 630 ft 2.

13. Given the scale factor, find the surface area of the similar prism. 1. The scale factor of the larger of two similar triangular prisms is 8. The surface area of the smaller prism is 18 ft 2. 2. The scale factor of the smaller of two similar triangular prisms is. 70 ft 2 1,152 ft 2 Insert Lesson Title Here Course 2 1313 The surface area of the larger prism is 630 ft 2.

14. Figures with the same volume but different shape. How many different rectangular prism have the volume of 36 cm 3 ? Volume formula l x w x h So what three numbers can be multiplied to make 36? 3 x 2 x 6 = 36 9 x 2 x 2 = 36 4 x 3 x 3 = 36

15. Figures with the same volume but different shape. How many different rectangular prism have the volume of 36 cm 3 ? Different shapes have different surface areas V = 3 x 2 x 6 = 36 cm 3 Surface area 3 x 2 x 2 = 12 2 x 6 x 2 = 24 3 x 6 x 2 = 32 Total Surface area 12 + 24 + 32 = 68 cm 2

16. Figures with the same volume but different shape. How many different rectangular prism have the volume of 36 cm 3 ? Different shapes have different surface areas V = 9 x 2 x 2 = 36 cm 3

17. Figures with the same volume but different shape. How many different rectangular prism have the volume of 36 cm 3 ? Different shapes have different surface areas V = 4 x 3 x 3 = 36cm 3

18. Practice Problems Pages 182-183 Odd #1-25