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

Answer:

The volume of the cone is 10 cubic units

Step-by-step 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

$V_c = \frac{1}{3} \pi r^2h$

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

$V_c = \frac{1}{3} \pi r^2h$ becomes

$V_c = \frac{1}{3} * 30$

$V_c = 10$

Hence, the volume of the cone is 10 cubic units