# The radius of the base of the cylinder is 6 cm, the height is half the circumference of the base. find the volume of the cylinder.

August 24, 2021 | education

| Given the condition:

h = C / 2,

where h is the height of the cylinder, C is the circumference of the base.

The circumference of the radius R is found by the formula:

С = 2πR,

where R is the radius of the circle (by condition R = 6 cm).

C = 2 * 6π = 12π (cm).

Let’s find the length of the cylinder height:

h = 12π / 2 = 6π (cm).

The volume of the cylinder is found by the formula:

V = Sh,

where S is the area of the base of the cylinder.

S = πR ^ 2;

S = 6 ^ 2 * π = 36π (cm square).

V = 36π * 6π = 216π ^ 2 (cm cubic).

Answer: V = 216π ^ 2 cm cubic.