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?
_ cm^3
To find the volume of the cylinder, we first need to find the radius and height of 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. Since the volume of the cone is 27 cm^3, we have:
27 = (1/3)πr^2h
Now, we also know that the volume of a cylinder is given by the formula V = πr^2h. Since the radius and height of the cylinder are the same as the cone, we can set up the equation:
V_cylinder = πr^2h
Since the volume of the cone is 27 cm^3, we can substitute for h in terms of r in the cone volume formula:
27 = (1/3)πr^2h
27 = (1/3)πr^2(3 * 27/πr^2)
27 = 3 * 27
27 = 27
Now we have the height of the cone in terms of the radius. We can substitute this into the formula for the volume of the cylinder:
V_cylinder = πr^2(3 * 27/πr^2)
V_cylinder = 81
Therefore, the volume of the cylinder that shares the same radius and height as the cone is 81 cm^3.