Question

Rewrite the formula to find the radius of a sphere. The volume (V) of a sphere is given by the formula . The sphere’s radius (r) is .

A.(3V/pi)1/3
B.4V/3pi)1/3
C.(3pi/4V)1/3

Answer 1

V = (4/3) pi r^3

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

r^3 = 3V / 4pi

r = (3V/4Pi)^(1/3)

Answer 2

Option C is correct

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

Explanation:

Volume of a sphere(V) is given by:

`V = (4)/(3) \pi r^3` .....[1]

where,

`3V = 4 \pi r^3`r is the radius of the sphere.

We have to find the radius r:

Multiply both sides by 3 both sides in [1] we have;

`3V = 4 \pi r^3`

Divide both sides by
`4\pi` we have;

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

Taking cube root both sides we have;

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

or

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

Therefore, the radius of the sphere is,
`\sqrt[3]{(3V)/(4 \pi)}` units