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 is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height of the cone.
We are given that the volume of the cone is 27 cm^3. So, we can write the equation as 27 = (1/3)πr^2h.
We are also given that the cone and the cylinder share the same radius and height. Therefore, the volume of the cylinder can be calculated using the formula V = πr^2h, where r and h are the same as the cone.
Since we have the equation 27 = (1/3)πr^2h, we can solve for h in terms of r by multiplying both sides by 3 and dividing by πr^2:
27 * 3 / (πr^2) = h
Now, we can substitute this value of h into the volume formula for the cylinder:
V_cylinder = πr^2 * (27 * 3 / (πr^2))
= 27 * 3
= 81 cm^3
Therefore, the volume of the cylinder that shares the same radius and height as the cone is 81 cm^3.