Question & Answer
QUESTION

The volume of a hemisphere is $2425\dfrac{1}{2}c{m^3}$. Find its curved surface area. $\left[ {\pi = \dfrac{{22}}{7}} \right]$

ANSWER Verified Verified
Hint: Here we first determine the radius of the hemisphere using the volume formula and then we find the curved surface area of the hemisphere.

Complete step-by-step answer:
Let the radius of the hemisphere = r
Given: Volume of hemisphere = $2425\dfrac{1}{2}c{m^3}$
$ \Rightarrow V = \dfrac{{4851}}{2}c{m^3}$
As we know the formula of volume of hemisphere is $ = \dfrac{2}{3}\pi {r^3}$
$ \Rightarrow \dfrac{2}{3}\pi {r^3} = \dfrac{{4851}}{2}$
$ \Rightarrow \dfrac{2}{3} \times \dfrac{{22}}{7}{r^3} = \dfrac{{4851}}{2}$
$ \Rightarrow {r^3} = \dfrac{{101871}}{{88}} \Rightarrow r = {\left( {\dfrac{{101871}}{{88}}} \right)^{\dfrac{1}{3}}} = 10.5cm$
The formula of curved surface area (CSA) of hemisphere is $ = 2\pi {r^2}$
$ \Rightarrow $ CSA = $2 \times \dfrac{{22}}{7} \times {\left( {10.5} \right)^2} = 693c{m^2}$
So, this is the required answer.

Note: To solve these types of problems, it is crucial to remember the basic formulae of the various parameters of various shapes to arrive at the answer faster. We should find the value of the terms (like radius here) connecting what is given and what we have to find.