Question

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

Answer 1

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`