The volume of a cone is 27 cm^3

. What is the volume of a cylinder that shares the same radius and height as the cone?

1 answer

To find the volume of a cylinder that shares the same radius and height as the cone, we can use the formula for the volume of a cone, which is 1/3 times the base area times the height.

Let's denote the radius of the cone as r and the height of the cone as h. We are given that the volume of the cone is 27 cm^3, so we have the equation:

(1/3)πr^2h = 27

To find the volume of the cylinder, we use the formula for the volume of a cylinder, which is the base area times the height. Since the cylinder shares the same radius and height as the cone, the volume of the cylinder is:

πr^2h

To find this value, we need to solve for r and h in the equation (1/3)πr^2h = 27.

First, let's isolate r^2h by multiplying both sides of the equation by 3:

πr^2h = 3 * 27

Simplifying, we have:

πr^2h = 81

Now, let's solve for h by dividing both sides of the equation by πr^2:

h = 81 / (πr^2)

Substituting this value for h into the equation for the volume of the cylinder, we have:

Volume of the cylinder = πr^2 * (81 / (πr^2))

Simplifying, we find that the volume of the cylinder is:

Volume of the cylinder = 81 cm^3.