
If the surface area of a hemisphere is ‘S’, then express ‘r’ in terms of ‘S’.
Answer
534.9k+ views
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.
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.
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