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?
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.