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.

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.