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?

Answer 1

The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height of the cone.

In this case, the volume of the cone is given as 27 cm^3. Let's assume the radius of the cone is r and the height is h.

So, we have the equation 27 = (1/3)πr^2h.

Now, let's find the volume of the cylinder with the same radius and height as the cone.

The volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height of the cylinder.

Since the cylinder shares the same radius and height as the cone, we can use the same values for r and h.

So, the volume of the cylinder = πr^2h.

Substituting the values of r and h from the cone equation, we get the volume of the cylinder = 3 * 27 = 81 cm^3.

Therefore, the volume of the cylinder that shares the same radius and height as the cone is 81 cm^3.