Mensuration - Sphere and Hemisphere

What is a Sphere?

A sphere is a three dimensional solid round structure, such that every point on its surface is equidistant from its center.

Hemisphere is the half of a sphere.

Formulae related to Sphere and Hemisphere

If ‘r’ is the radius, and ’d’ is the diameter of a sphere/hemisphere, then:

Formula 1: Volume

Volume of sphere = $\frac{4}{3} πr^3$ = $\frac{1}{6} πd^3$

Volume of hollow sphere = Volume of whole sphere - Volume of inner empty space = $\frac{4}{3} πR^3 - \frac{4}{3} πr^3 = \frac{4}{3} π (R^3 – r^3) = \frac{1}{6} π (D^3 – d^3)$
(where R - external radius of sphere, r - internal radius of sphere)

Volume of hemisphere = $\frac{2}{3} πr^3$ = $\frac{1}{6} πd^3$

Formula 2: Surface Area

Surface area of sphere = 4π$r^2$ = π$d^2$

Curved Surface area of hemisphere = 2π$r^2$

Total Surface area of hemisphere = 2π$r^2 + πr^2 = 3πr^2$