A sphere is a three-dimensional figure obtained by the revolution of a semicircle about its diameter as an axis.
shutterstock_1712835637 (1).jpg
Volume of a sphere:
Let \(r\) be the radius of a sphere.
Volume of a sphere \(=\) 43πr3 cu. units
shutterstock_1885382680 (1).jpg
Demonstration of the volume of a sphere using right circular cones:
Let us take a sphere and two right circular cones of the same base radius and height.
sp_cone (1).png
Radius of a sphere \(=\) \(r\) units
Radius of two cones  \(=\) \(r\) units
Height of a sphere \(=\) Diameter \(=\) \(2r\)
Height of each cone \(=\) Height of a sphere \(=\) \(2r\)
Volume of a sphere \(=\) Volume of \(2\) cones
\(=\) 2×13πr2h
\(=\) 2×13πr2×2r [Since \(h = 2r\)]
\(=\) 43πr3
Volume of a sphere \(=\) 43πr3 cu. units
Volume of a hollow sphere / spherical shell (volume of the material used):
hol_sp (1).png
Let \(r\) be the inner radius and \(R\) be the outer radius of the hollow sphere.
Volume of a hollow sphere \(=\) Volume enclosed between the outer and inner spheres
\(=\) 43πR3 \(-\) 43πr3
\(=\) 43πR3r3
Volume of a hollow sphere \(=\) 43πR3r3 cu. units
The value of \(\pi\) should be taken as 227 unless its value is shared in the problem.