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 point)
The volume of a cone is given by the formula: V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
We know that the volume of the cone is 27 cm^3. Plugging this into the formula, we get:
27 = (1/3)πr^2h
Now, let's find the volume of the cylinder. The volume of a cylinder is given by the formula: V = πr^2h, where V is the volume, r is the radius, and h is the height.
Since the radius and height of the cone and cylinder are the same, we can write:
V_cylinder = πr^2h
To find the volume of the cylinder, we just need to determine the value of πr^2h. We already know that 27 = (1/3)πr^2h, so multiplying both sides of this equation by 3/π gives:
81/π = r^2h
Therefore, the volume of the cylinder is 81/π cm^3.