Question

If the surface area of a hemisphere is ‘S’, then express ‘r’ in terms of ‘S’.

Answer 1

Hint: Curved Surface Area (CSA) of hemisphere$S = 2\pi {r^2}$

Surface area is Curved surface area.
Curved Surface Area (CSA) of a Hemisphere is given by the formula$S = 2\pi {r^2}$ …(1)
We have to express ‘r’ in terms of ‘S’. So, by rearranging equation (1), we get
$\begin{gathered}
  S = 2\pi {r^2} \\
  {r^2} = \dfrac{S}{{2\pi }} \\
  r = \sqrt {\dfrac{S}{{2\pi }}} \\
\end{gathered} $
 The required formula is $r = \sqrt {\dfrac{S}{{2\pi }}} $
Note: If ‘Total’ surface area is mentioned in the question, the formula will differ. Look for
small word changes in the questions which can make a big difference to the solution.