EXAMPLE 1 Find the volume of a solid

Find the volume of the solid.

V = Bh13

= 36 m3

a.

= ( 4 6)(9)13

12

EXAMPLE 1 Find the volume of a solid

V = Bh13

= (πr2)h13

= 7.26π ≈ 22.81 cm3

b.

= (π 2.22)(4.5)13

EXAMPLE 2 Use volume of a pyramid

ALGEBRA

Originally, the pyramid had height 144 meters and volume 2,226,450 cubic meters. Find the side length of the square base.

SOLUTION

V = bh1

3Write formula.

2,226,450 = (x2)(144)1

3Substitute.

EXAMPLE 2 Use volume of a pyramid

6,679,350 = 144x2 Multiply each side by 3.

46,384 ≈ x2 Divide each side by 144.

215 ≈ x Find the positive squareroot.

Originally, the side length of the base was about 215 meters.

ANSWER

GUIDED PRACTICE for Examples 1 and 2

Find the volume of the solid. Round your answer to two decimal places, if necessary.

1. Hexagonal pyramid

SOLUTION

Volume is v = bh1

3Area of a hexagon of base 4 is 41.57

v = bh1

3= (41.57)(11)

1

3= 152.42 yd3

GUIDED PRACTICE for Examples 1 and 2

2. Right cone

SOLUTION

Value of a cone is v = bh1

3

First find by Pythagorean method

GUIDED PRACTICE for Examples 1 and 2

v = bh1

3Write formula.

Substitute.h = (82) (5)2–

= 6.24

= (π 52)(6.24)1

3

= 163.49m3

Simplify

Substitute.

Simplify

GUIDED PRACTICE for Examples 1 and 2

3. The volume of a right cone is 1350π cubic meters and the radius is 18 meters. Find the height of

the cone.

SOLUTION

V = bh13

1350π = (π182)h13

4050π = π(18)2 h

12.5 = h

Write formula.

Substitute.

Multiply each side by 3.

Divide each side by 324 π.

The Height of the cone is 12.5mANSWER