Volume of hemisphere — lesson. Mathematics CBSE, Class 9.

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Hemisphere:

A 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

Example:

The radius of the hemisphere is

$14 \ cm$ . Find the volume of the hemisphere in grams if

$1 \ cm^3 = 0.4 \ g$ .

Solution:

Radius of the hemisphere

$(r)$

$=$

$14 \ cm$

Volume of the hemisphere

$=$

$\frac{2}{3} π r^{3}$ cu. units

$=$

$\frac{2}{3} \times \frac{22}{7} \times 14^{3}$

$=$

$\frac{2}{3} \times \frac{22}{7} \times 14 \times 14 \times 14$

$=$

$5749.33$

$cm^3$

Now, convert

$cm^3$ to

$g$ .

$1 \ cm^3$

$=$

$0.4 \ g$

$5749.33 \ cm^3$

$=$

$5749.33 \times 0.4$

$=$

$2299.732 \ g$

Therefore, the volume of the hemisphere is

$2299.732 \ g$ .

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: