Compare Volumes of 3D shapes

The volumes of a cone, a cylinder, and a hemisphere with the same radius are compared.

Problem

• (a) A cone with height \( r \) and radius of the base \( r \)
• (b) A cylinder of height \( r \) and radius of the base \( r \)
• (c) A hemisphere of radius \( r \)

• Volume (\(V_{\text{co}}\)) of the cone is given by: \[ V_{\text{co}} = \frac{1}{3} \times \text{area of base} \times \text{height} = \frac{1}{3} \pi r^2 \times r = \frac{1}{3} \pi r^3 \]
• Volume (\(V_{\text{cy}}\)) of the cylinder is given by: \[ V_{\text{cy}} = \text{area of base} \times \text{height} = \pi r^2 \times r = \pi r^3 \]
• Volume (\(V_{\text{he}}\)) of the hemisphere is given by: \[ V_{\text{he}} = \frac{1}{2} \times \text{volume of a sphere} = \frac{1}{2} \times \frac{4}{3} \pi r^3 = \frac{2}{3} \pi r^3 \]
• The volume of the cylinder is the largest. The volume of the cone is one third of the volume of the cylinder and it is the smallest. The volume of the hemisphere is twice the volume of the cone or two thirds the volume of the cylinder.

More References and Links to Geometry