The volume of a hemisphere is 2425 $\frac{1}{2}$ cm³^. Find its curved surface area.
$[Use π = \frac{22}{7}]$

Solution

Given: Volume of a hemisphere = 2425 $\frac{1}{2}$ cm³ = $\frac{4851}{2}$ cm³.

Now, let r be the radius of the hemisphere

Volume of a hemisphere = $\frac{2}{3} {πr}^{3}$

$∴ \frac{2}{3} {πr}^{3} = \frac{4851}{2} \Rightarrow \frac{2}{3} x \frac{22}{7} x r^{3} = \frac{4851}{2} \Rightarrow r^{3} = \frac{4851}{2} x \frac{3}{2} x \frac{7}{22} = {(\frac{21}{2})}^{3} ∴ r = \frac{21}{2} cm$

So, curved surface area of the hemisphere = $2 {πr}^{2}$

= $2 x \frac{22^{11}}{7} x \frac{21^{3}}{2} x \frac{21}{2}$

= 693 sq. cm.

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The volume of a hemisphere is 2425 $\frac{1}{2}$ cm³^. Find its curved surface area.
$[Use π = \frac{22}{7}]$