If the total surface area of a solid hemisphere

Asked by admin @ 17/08/2021 in Math viewed by 352 People

If the total surface area of a solid hemisphere is 462 sq cm , find its volume.

Answered by admin @ 17/08/2021

Answer:

Its volume is $718.67 cm^3$

Step-by-step explanation:

Formula of total surface area of hemisphere : $3 \pi r^2$

So, total surface area of hemisphere = $3 \times \frac{22}{7} \times r^2$

We are given that the total surface area of a solid hemisphere is 462 sq cm.

So, $3 \times \frac{22}{7} \times r^2=462$

$r^2=462 \times \frac{7}{22 \times 3}$

$r=\sqrt{462 \times \frac{7}{22 \times 3}}$

$r=7$

So, Radius of hemisphere is 7 cm.

Volume of hemisphere = $\frac{2}{3} \pi r^3$

= $\frac{2}{3} \times \frac{22}{7} \times (7)^3$

= $718.67 cm^3$

Hence its volume is $718.67 cm^3$

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