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: