Question

The cylinder shown has a volume of 30 cubic units.The come and the cylinder have the same height and the same base.What is the volume of the cone?

Answer 1

The volume of the cone is 10 cubic units

Explanation:

Given

Solid Shapes: Cone and Cylinder

Volume of Cylinder = 30 cubic units

Required

Volume of Cone

From the question; we have that the cylinder and the cone has the same height (h) and the same base;

Since they have the same base, then this means they have the same radius.

The Volume (V) of a cylinder is calculated as follows

`V = \pi r^2h`

Substitute 30 for V

`30 = \pi r^2h`

The Volume (Vc) of a cylinder is calculated as follows

`V_c = (1)/(3) \pi r^2h`

From the volume of a cone, we have that
`\pi r^2h = 30`; This means that we can substitute 30 for
`\pi r^2h`

`V_c = (1)/(3) \pi r^2h` becomes

`V_c = (1)/(3) * 30`

`V_c = 10`

Hence, the volume of the cone is 10 cubic units