Question

A hemispherical tank has an inner radius of $2.8m$. Find its capacity in litres.

Answer 1

Hint: We will simply find the volume of the hemisphere having radius $2.8m$. This volume will tell us about the capacity of the hemisphere in litres. Volume of hemisphere $=\dfrac{2}{3}\pi {{r}^{3}}$.

Complete step-by-step answer:
It is given in the question that we have a hemispherical tank of inner radius $2.8m$. We have to find the capacity of tanks in litres. We know that the volume of the hemisphere is given by formula $\dfrac{2}{3}\pi {{r}^{3}}$.
So, on substituting the value of $r$ as $2.8m$ in the formula of volume of hemisphere, we get
Volume of hemisphere $=\dfrac{2}{3}\pi {{r}^{3}}$
$=\dfrac{2}{3}\pi {{(2.8)}^{3}}$
$=\dfrac{2}{3}\pi (2.8)(2.8)(2.8)$
$=\dfrac{2}{3}\times \dfrac{22}{7}\times 21.952$
$=\dfrac{44}{21}\times 21.952$
$=\dfrac{965.88}{21}$
$=45.9946{{m}^{3}}$
Thus, the volume of the hemisphere is $45.99{{m}^{3}}$ (approx.)
Now, we have to find the capacity of tanks in litres. We will convert the volume of the hemispherical tank into litres. We will use a unitary method to find the number of litres in $45.99{{m}^{3}}$. Firstly find the value of a single unit then find the required value by multiplying the value of a single unit with the volume of the hemisphere.
We know that, $1{{m}^{3}}=1000l$, from this we can find the value,
Capacity of tank $=45.99{{m}^{3}}\times 1000l$
$=45990lit.$
Thus, the capacity of hemispherical tank is $45990lit.$

Note: Hemisphere is the half cut shape of the sphere, the volume of the sphere is given by $\dfrac{4}{3}\pi {{r}^{3}}$.
From this, we get the volume of hemisphere $=\dfrac{4}{3}\times \dfrac{\pi {{r}^{3}}}{2}$
$=\dfrac{2}{3}\pi {{r}^{3}}$.
Also, to convert ${{m}^{3}}$ into litres we can directly multiply ${{m}^{3}}$ value with $1000l$.