Question

The volume of a sphere is 32/3 π cubic centimeters. What is the radius?

Sphere V = 4/3 πr3

1. Substitute 32/3 into the volume formula for V:    32/3 π = 4/3
πr3

2. Multiply both sides of the equation by 3/4: 8π = πr3

3. Divide both sides of the equation by π. 8 = r3

4. Take the cube root of both sides:          3√8 = r

The radius of the sphere is
cm.

Answer 1

The radius of the sphere is 2 cm.

Explanation:

Answer 2

The radius of the sphere is 2 cm

Explanation:

To find the radius of a sphere with a volume of 32/3 π cubic centimeter, we will follow the steps below,

First write down the formula for calculating the radius of the sphere.

That is;

V=
`(4)/(3)` πr³

where v is the volume of the sphere and r is the radius of the sphere.

From the question given volume is equal to 32/3 π cubic centimeters.

Substitute for v in the formula and solve for r

V=
`(4)/(3)` πr³

`(32)/(3)` π =
`(4)/(3)` πr³

The π at the left-hand side will cancel-out the π on the right-hand side of the equation.

`(32)/(3)` =
`(4)/(3)` r³

Multiply both-side of the equation by
`(3)/(4)`

`(32)/(3)` ×
`(3)/(4)` =
`(3)/(4)`×
`(4)/(3)` r³

8=r³

Take the cube root of both-side of the equation

∛8=∛r³

2 = r

r = 2 cm

Therefore the radius of the sphere is 2 cm