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