1. Unit 5 Lesson 8 Unit Review

2. If a number is a perfect cube, then you can find its exact cube root. A perfect cube is a number that can be written as the cube (raised to third power) of another number. Perfect Cubes

3. Examples :

4. Converting cubic units 1 ft 3 = 1728 in 3 1 yd 3 = 27 ft 3 1 cm 3 = 1000 mm 3 1 m 3 = 1000000 mm 3

5. Converting cubic units 8 yd 3 = ft 3 12 cm 3 = mm 3

6. Volume Volume (rectangular prism) Formula: B = l x w V = B x h V = l x w x h l w h

7. Volume Find the volume of this prism… Formula: V = B x h V = l x w x h 5 cm 4 cm 7 cm

8. Volume Volume B = ½ bh V = B x h V = (8 x 4) x 12 2 V = 16 x 12 V = 192 cm 3

9. Volume Your turn… Find the Volume

10. What solid figure can be made with this net? cube

12. What solid figure can be made with this net? square pyramid

13. Pyramid

14. What solid figure can be made with this net? triangular prism

15. Triangular prism

16. Surface Area – Basic concept Determine the number and shape of the surfaces that make up the solid. It might be easier to think of the net of the solid. square rectangle square rectangle 4 rectangular faces and 2 square faces When you’ve done all that find the area of each face and then find the total of the areas.

17. Square prism 18 cm Two square faces Find the surface area of this figure with square base 5 cm and  height 18 cm 5 cm Four rectangular faces

18. Triangular Prism 12 cm 20 cm 10 cm Hence, total surface area Find the surface area of this figure with dimensions as marked. 12 cm 10 cm 6 8 Use Pythagoras’ theorem to find the  height of the triangle! Determine the number of faces and the shape of each face Apply the area formulae for each face Sum the areas to give the total surface area

19. Square Pyramid Find the surface area of this figure with square base 10 cm and  height 12 cm. 4 triangular faces with the same dimensions and 1 square face We need to find the  height of each triangular face. 10 13 T P  Each triangular face will have base 10 cm and  height 13 cm. 12 Hence, total surface area

20. 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!

21. 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.

22. 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

23. 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.

24. Figures with the same volume but different shape. How many different rectangular prism have the volume of 64 cm 3 ? Different shapes have different surface areas V = 16 x 2 x 2 = 64 cm 3 ___x___x___x = 64

25. Practice Problems Pages 184-185 #1-24 Kmail me any problems you need help on and I will use them in Tuesday‘s class Connect Session