Question

The radius of a wooden hemisphere is 10 cm. What is its volume?
If this hemisphere is curved into a cone of maximum size, find the volume of the cone.

Answer 1

Radius of the hemisphere $=10\text{cm}$
Volume of the hemisphere $=\frac{2}{3}\pi r^3$

$=\frac{2}{3}\times \pi \times (10{)}^3$

$=\frac{2000}{3}\pi {\text{cm}}^3$
When the hemisphere is curved into a cone of maximum size, its base radius is $10\text{cm}$ and height is $10\text{cm}$.
Volume of the cone $=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\times \pi \times (10{)}^2\times 10$

$=\frac{1000}{3}\pi {\text{cm}}^3$