The volume of a sphere is 367 ft. What is the radius of the sphere? Use the formula V = ar to find your answer.

Question

asked Oct 4, 2022 199k views

1 Answer

Pbanka · Answer 1 · 2022-10-09T13:54:52+0000

Answer:

Answer: Radius is 3 ft

Explanation:

Formular:

${ \boxed{V = (4)/(3) \pi {r}^(3) }} \\$

substitute:

$36\pi = (4)/(3) \pi {r}^(3)$

multiply all sides by 3:

$(36\pi * 3) = ( (4)/(3) \pi {r}^(3) ) * 3 \\ \\ 108\pi = 4\pi {r}^(3)$

divide all sides by π :

$(108\pi)/(\pi) = \frac{4\pi {r}^(3) }{\pi} \\ \\ 108 = 4 {r}^(3)$

divide all sides by 4:

$(108)/(4) = \frac{4 {r}^(3) }{4} \\ \\ {r}^(3) = 27$

take a cube root:

$\sqrt[3]{ {r}^(3) } = \sqrt[3]{27} \\ r = \sqrt[3]{(3 * 3 * 3)} \\ r = \sqrt[3]{ {3}^(3) } \\ \\ r = 3$