Question

What is the diameter of a sphere with a volume of 18174 ft^3 to the nearest tenth of a foot?

Answer 1

Diameter = 33 feet

Explanation:

Diameter = 2 x radius

Given that the volume = 18174
`ft^(3)`, then;

Volume of sphere =
`(4)/(3)`
`\pi`
`r^(3)`

where r is the radius of the sphere.

Thus,

18174 =
`(4)/(3)` x
`(22)/(7)` x
`r^(3)`

=
`(88)/(21)`
`r^(3)`

18174 x 21 = 88
`r^(3)`

381654 = 88
`r^(3)`

`r^(3)` =
`(381654)/(88)`

= 4336.9773

r =
`\sqrt[3]{4336.9773}`

r = 16.3078

The diameter of the sphere = 2 x 16.3078

= 32.6156

= 33 feet