The volume of a cylinder is 60 cm^3. What is the volume of a cone that shares the same radius and height as the cylinder
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
Since the cylinder and cone share the same radius and height, let's assume r is the radius and h is the height of both shapes.
Given that the volume of the cylinder is 60 cm^3,
V_cylinder = πr^2h = 60
The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius and h is the height.
Since the cone and cylinder share the same radius and height,
V_cone = (1/3)πr^2h
But we know that the volume of the cylinder is 60 cm^3,
so (1/3)πr^2h = 60
Multiplying both sides by 3 and dividing by π, we get:
r^2h = 180/π
Thus, the volume of the cone is also 180/π cm^3.