Question

Question 1
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of $\pi$.

Answer 1

Radius = 1 cm, height = 1 cm
Volume of hemisphere
$=\frac{2}{3}\pi r^3$
$=\frac{2}{3}\pi \times 1^3$$=\frac{2}{3}\pi c{m}^3$
Volume of cone
$=\frac{1}{3}\pi r^{2}h$
$=\frac{1}{3}\pi \times 1^2\times 1$
$=\frac{1}{3}\pi c{m}^3$
Total volume
$=\frac{2}{3}\pi +\frac{1}{3}\pi =\pi c{m}^3$