Question

What is the volume of a sphere with a surface area of 25pi / (d ^ 2)

Answer 1

B.
`(125)/(6)* \pi` yd³

Explanation:

Given:

Surface area of a sphere = 25π yd²

Required:

Volume

Solution:

Let's find the radius (r) first.

S.A of sphere = 4πr²

Substitute

25π = 4πr²

Divide both sides by 4π

25π/4π = r²

25/4 = r²

Take the square root of both sides

√25/√4 = r

5/2 = r

r = 5/2 yd

Find the Volume of the sphere

V = ⁴/3*πr³

V = ⁴/3*π*(⁵/2)³

V = ⁴/3*π*125/8

V = ⅓*π*125/2

V =
`(1*125)/(3*2)* \pi`

V =
`(125)/(6)* \pi` yd³