Volume of hemisphere — lesson. Mathematics State Board, Class 10.

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Hemisphere:

A section of the sphere cut by a plane through any of its great circles is a hemisphere. In another way, we can say, one half of a sphere is called a hemisphere.

Volume of a hemisphere:

Let

$r$ be the radius of a sphere.

Volume of a hemisphere

$=$

$\frac{1}{2}$

$\times$ Volume of a sphere

$=$

$\frac{1}{2} \times (\frac{4}{3} π r^{3})$

$=$

$\frac{2}{3} π r^{3}$

Volume of a hemisphere

$=$

$\frac{2}{3} π r^{3}$ cu. units

Volume of hollow hemisphere (volume of the material used):

Let

$r$ be the inner radius and

$R$ be the outer radius of the hollow hemisphere.

Volume of hollow hemisphere

$=$ Volume of the outer hemisphere

$-$ Volume of the inner hemisphere

$=$

$\frac{2}{3} π R^{3}$

$-$

$\frac{2}{3} π r^{3}$

$=$

$\frac{2}{3} π (R^{3} - r^{3})$

Volume of a hollow hemisphere

$=$

$\frac{2}{3} π (R^{3} - r^{3})$ cu. units

Important!

The value of

$\pi$ should be taken as

$\frac{22}{7}$ unless its value is shared in the problem.

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2. Volume of hemisphere

Theory: