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.

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 ½ x 5 =152.5

5. Drill
450÷20 = 22.5

6. Drill
50½ 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

11. Review
Rectangular
Prism

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 ∏r2
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 ⅓Bh = ⅓(18 × 8) = 48 cm3.
The volume of all three pyramids combined equals 144 cm3. The
volume of the rectangular prism is equal to Bh = 18 × 8 = 144 cm3

29. The volume of a Rectangular Prism and a Pyramid

30. GROUP ACTIVITY
Group I – Construct a prism and a pyramid with same base and
height
Group II – Solve for the volume of the two figures using the
formula.
Group III – Compose a rap song about the relationship of the
volume of rectangular prism and pyramid
Group IV – 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.