what is the height of a cone with a volume of 66 cubic centimeters and a base with a radius of 3 centimeters

volume of cone = (1/3)πr^2h

66 = (1/3)π(9)h
h = 198/(9π) = 22/π

To find the height of a cone with a given volume and base radius, you can use the formula for the volume of a cone:

Volume = (1/3) * π * r^2 * h,

where "r" is the radius of the base and "h" is the height of the cone.

In this case, the volume is given as 66 cubic centimeters and the base radius is 3 centimeters. Let's substitute these values into the formula and solve for the height.

66 = (1/3) * π * 3^2 * h.

First, simplify the equation:

66 = (1/3) * 9 * π * h.

Now, multiply 9 and π/3:

66 = 3π * h.

Next, divide both sides by 3π to isolate "h":

66 / (3π) = h.

Simplify further by using an approximation for π, such as 3.14:

h ≈ 66 / (3 * 3.14).

Now, calculate the height:

h ≈ 7.03 centimeters.

Therefore, the height of a cone with a volume of 66 cubic centimeters and a base radius of 3 centimeters is approximately 7.03 centimeters.