Question

The volume, V, of a sphere in terms of its radius, r, is given by V (r) = 77³. Express r as a function

of V, and find the radius of a sphere with volume of 400 cubic feet.
Round your answer for the radius to two decimal places.

r(V)= ____
A sphere with volume 400 cubic feet has radius _____feet.

Answer 1

`r = \sqrt[3]{(3V)/(4 \pi)}`

r = 4.57 ft

Explanation:

`V = (4)/(3) \pi r^3`

`(4)/(3)\pi r^3 = V`

`\pi r^3 = (3)/(4) V`

`r^3 = (3V)/(4 \pi)`

`r = \sqrt[3]{(3V)/(4 \pi)}`

`r = \sqrt[3]{(3 * 400)/(4 \pi)}`

`r = \sqrt[3]{(300)/(\pi)}`

`r = 4.57078`

r = 4.57 ft