Question

A storage tank consists of a circular cylinder with a hemisphere adjoined at either end. If the external diameter of the cylinder is $1.4m$ and its length be $8m$, find the cost of painting it on the outside at the rate of $Rs.10per{m^2}$.

Answer 1

Hint: Since on the circular cylinder a hemisphere is adjoined on either end and we need to find out the cost of painting the cylinder from outside.
Hence, we have to calculate the Surface areas i.e.
Surface area of the tank=Surface area of cylinder + Surface area of the hemisphere.
Surface area of the tank= $2\pi rh + 2\pi {r^2}$

Complete step-by-step answer:
Let us draw the figure according to the question.
Given that, the external diameter of the cylinder is $1.4m$ and the length of the cylinder is $8m$.
Also a hemisphere is adjoined at either end whose radius will be the same as the radius of the cylinder.
So we obtain the figure as given below:

Here, the radius ($r$) of the sphere=radius of cylinder=$\dfrac{{diameter}}{2}$
$ = \dfrac{{1.4}}{2} = 0.7m$
According to the question,
Surface area of the tank=Surface area of cylinder + Surface area of the hemisphere.
Surface area of the tank= $2\pi rh + 2\pi {r^2}$
$ \Rightarrow 2\pi r(h + r)$
Now substituting the value of$\pi = \dfrac{{22}}{7}$, $h = 8$and $r = 0.7$we get,
$ = 2 \times \dfrac{{22}}{7} \times 0.7 \times (8 + 0.7)$
$ = 2 \times \dfrac{{22}}{7} \times 0.7 \times 8.7 = 38.28{m^2}$
Now we have to calculate the cost of painting it on the outside at the rate of $Rs.10per{m^2}$.
$ = Rs(38.28 \times 10)$
$ = Rs382.80$

Note: Surface area of the tank= $2\pi rh + 2\pi {r^2}$
We have external diameter of the cylinder =$1.4m$
We can calculate radius of the cylinder=$\dfrac{{diameter}}{2}$
To calculate the cost of painting the cylinder from outside simply multiply the surface area with the given rate of $per {m^2}$.