Given a sphere with a surface area of 256pi square units, find its EXACT volume.

volume of the sphere =   2143.57units³

Step-by-step explanation:

Given that the area of a sphere = 256πunits²

volume of the sphere = ?

recall that the area of a sphere = 4πr²

256π = 4 πr²

divide both sides by 4π

256π/4π = 4πr²/4π

64 = r²

squaring both sides

r = √64

r = 8units

now to calculate the volume of the sphere,

recall that

volume of the sphere =  4π r³/3

volume of the sphere =  4π 8³/3

volume of the sphere =  4π 512/3

volume of the sphere =  4 × 3.14 × 170.667

volume of the sphere =   2143.57units³

1520.5 cm³

Step-by-step explanation:

Volume formula for cylinder: V = πr²×h

Radius = 11 ÷ 2

           = 5.5cm

Volume = π × 5.5² × 16

             =1520.5cm³