A cylinder with a base diameter of x units has a volume of πx³ cubic units. which statements about the cylinder are

true? select two options.

the radius of the cylinder is 2x units.

the area of the cylinder's base is ¼πx² square units.

the area of the cylinder's base is ½πx² square units.

the height of the cylinder is 2x units.

the height of the cylinder is 4x units.

Answer: the area of the cylinder's base is ¼πx² square units.

the height of the cylinder is 4x units.

Step-by-step explanation:

The The formula for determining the volume of a cylinder is expressed as

Volume = πr²h

Where

r represents the radius of the cylinder.

h represents the height of the cylinder.

π is a constant

From the information given,

Volume = πx³ cubic units

Base diameter = x units

Radius = diameter/2 = x/2

Therefore,

Area of a circle = πr²

Since the base is a circle, then

Area of circular base = π * (x/2) ²

= 1/4πx² square units

Height = volume/πr²

Since

Volume = πx³

Then

Height = πx³ / (1/4πx²)

= πx³ * 4/πx²

= 4x units