6th Grade Math Textbook, Fundamentals

Lesson 11-8 for exercise sets. &KDSWHU 

3UDFWLFH   $FWLYLWLHV

Find the volume of each pyramid.

1.Rectangular pyramid: 2.Triangular pyramid:

3 m; w18 m; h14 m base of base 6 yd; height of base 4 yd;

height of pyramid 9yd

Find the unknown dimension.

3.Triangular pyramid: 4.Rectangular pyramid:

V140 m^3 ; height of pyramid 15 m; V12,852 in.^3 ; ?; w17 in.; h36 in.

base of base 8 m; height of base ?

5.Discuss and Write Why is the slant height nota part of the

formula to find the volume of a square pyramid?

1

3

1

2

A square pyramid has a base that

measures 10 ft on each side. Its height is

21 ft. What is the pyramid’s volume?

V Bh

 (w)h

 (10 • 10)21

 (100)

 (100)  725

So the pyramid’s volume is 725 ft^3.

1

3

29

4

87

4

3

4

1

3

1

3

1

3

3

4

(^1) A triangular pyramid has a volume of 1618.2 cm^3.
Its base has a height of 15.5 cm and a base of
18 cm. What is the pyramid’s height?
V Bh
1618.2  ( bhbase)hpyramid
1618.2  ( • 18 • 15.5)h
1618.2  (139.5)h
1618.2 46.5h
34.8 h
So the pyramid’s height is 34.8 cm.
1
3
1
3
1
2
1
2
1
3
1
3
2

If you know the volume of a pyramid, you can use formulas and

algebra to solve for an unknown dimension of the pyramid.

The rectangular pyramid at the right has a volume of

160.65 cubic meters. What is the width of its base?

V Bh Formula for the volume of a pyramid

 (w)h Substitute the formula for the area of a rectangle for B.

160.65 (8.5w)9 Substitute known values.

160.65 3(8.5w) Use the Commutative Property to simplify.

 Divide both sides by 25.5 to isolate w.

6.3 w

So the rectangular base of the pyramid has a width of 6.3 meters.

1 3 1 3 1 3

25.5w

25.5

160.65

25.5

w

h  9 m

  8.5 m