Determines the relationship between a rectangular prism and a pyramid
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The document discusses the relationship between the volumes of rectangular prisms and pyramids. It states that the volume of a pyramid is equal to 1/3 the volume of a rectangular prism with the same base area and height. The volume of a rectangular prism is calculated by multiplying the base area by the height, while the volume of a pyramid uses 1/3 of the base area times the height. Several examples are provided to demonstrate calculating the volumes of prisms and pyramids.
Determines the relationship between a rectangular prism and a pyramid
- 1. Determines the relationship of the volume between a rectangular prism and a pyramid.
- 2. Drill 35 x 25 = 875
- 3. Drill 125 x 2.5 =312.5
- 4. Drill 30 ? x 5 =152.5
- 6. Drill 50? x 15= 757.5
- 7. Drill s = 25 cm Surface Area of a Cube S.A = (s x s) x 6
- 8. Drill S.A = (s x s) x 6 S.A= (25 x 25) x 6 S.A= 625 x 6 S.A= 3 750 cm2
- 9. Drill l = 16 cm, w = 9cm, h =8cm Surface Area of a Rectangular Prism S.A = (2l+2w) x h + 2 (Llx W)
- 10. Drill S.A = (2l+2w) x h + 2 (l x W) S.A= 2(16) + 2(9) x 8 + 2(9x16) S.A= (32+18) x8 + 2 (144) S.A= 50 x 8 + 288 S.A= 400 + 288 S.A= 688 cm2
- 12. Review Sphere
- 13. Review Cone
- 14. Review Cylinder
- 15. Review Pyramid
- 16. Review Cube
- 17. Review A rectangular box has a length of 14 inches, a width of 9 inches and a height of 15 inches. What is the surface area?
- 18. Answer S.A = (2l+2w) x h + 2 (l x w) S.A = 2 (14) + 2 (9) x 15 +2 (14 x 9) S.A = (28 + 18) x 15 + 2 (126) S. A = 46 x 15 + 252 S.A = 690 + 252 S.A = 942 inch2
- 19. Review A sphere has a radius of 9 cm. What is the surface area?
- 20. Answer S.A = 4 ¡Çr2 S.A = 4 (3.14)(9) (9) S.A = 12.56 x 81 S.A = 1017.36 cm2
- 23. Volume of a Prism
- 24. Volume of a Prism Volume of prism = is the product of the base area (B) and the height (h). V= B x h Since B=l x w, then V=l x w x h V= 5cm x 5cm x 5cm V= 625 cm3
- 25. Volume of a Prism Formula: V = l x w x h
- 26. Volume of a Pyramid Complete the statement: Volume of the pyramid= ______x volume of rectangular prism. For a rectangular prism, V= l x w x h So for pyramid, V= _____ l x w x h Or V= l x w x h ? The volume of a pyramid is 1/3 the volume of a prism w/ same base area (B) and height (h).
- 27. Volume of a Pyramid Formula: V = 1/3 x l x w x h
- 28. The volume of a Rectangular Prism and a Pyramid The volume of each pyramid is equal to ?Bh = ?(18 ¡Á 8) = 48 cm3. The volume of all three pyramids combined equals 144 cm3. The volume of the rectangular prism is equal to Bh = 18 ¡Á 8 = 144 cm3
- 29. The volume of a Rectangular Prism and a Pyramid
- 30. GROUP ACTIVITY Group I ¨C Construct a prism and a pyramid with same base and height Group II ¨C Solve for the volume of the two figures using the formula. Group III ¨C Compose a rap song about the relationship of the volume of rectangular prism and pyramid Group IV ¨C Dramatize the importance of the volume of solid figures (rectangular prism and pyramid) as we apply it in daily living.
- 31. GROUP PRESENTATION VOLUME OF RECTANGULAR PRISM AND PYRAMID
- 32. Application Find the volume of the following: 6cm 5cm4cm
- 33. GENERALIZATION Volume of prism = is the product of the base area (B) and the height (h). The volume of a pyramid is 1/3 the volume of a prism w/ same base area (B) and height (h). V= B x h or V= l x w x h V= 1/3 x B x h or V= 1/3 x l x w x h
- 34. Application Read and solve: Find the volume of a rectangular prism and square pyramid with the same base of 6 cm by 4 cm and a height of 10 cm.
- 35. Assessment Find the volume of the following figures. Write and compare the formula used in solving the problem c)
- 36. Assignment Make a paper pyramid, cube or prism using coloured paper.