The surface area of a sphere is 64π cm². what is the volume of the sphere?

The answer is 85.33π cm³

A) Calculate the radius of the sphere using the formula for the surface area.
B) Calculate the volume of the sphere using the radius.

A) The surface area (A) of a sphere with radius r is:
A = 4π r²

If A = 64π cm², then:
64π cm² = 4π r²

Divide both sides by π:
64π cm² /π = 4π  /π
64 cm² = 4r²
r² = 64 cm²/4
r² = 16 cm²
r = √16 cm²
r = 4 cm

B) The volume (V) of the sphere is:
V = 4/3 π r³
V = 4/3 π (4 cm)³
V = 4/3 π 64 cm³
V = 85.33π cm³