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

 Given:

A storage tank consists of a circular cylinder with a hemisphere adjoined on either end.

The external diameter of the cylinder is $1.4\ m$ and its length is $8\ m$.

To do:

We have to find the cost of painting it on the outside at the rate of $Rs.\ 10$ per $m^2$.

Solution:

Diameter of the tank $= 1.4\ m$

This implies,

Radius of the tank $(r) =\frac{1.4}{2}$

$= 0.7\ m$

Height of the cylindrical portion $(h)= 8\ m$

Therefore,

Outer surface area of the tank $=2 \pi r h+2 \pi r^{2}$

$=2 \pi r(h+r)$

$=2 \times \frac{22}{7} \times 0.7(8+0.7)$

$=\frac{2 \times 22 \times 7}{7 \times 10}(8.7)$

$=\frac{44}{10} \times 8.7$

Rate of painting $=Rs.\ 10$ per $\mathrm{m}^{2}$

Total cost of painting $=Rs.\ \frac{44 \times 8.7 \times 10}{10}$

$=Rs.\ 382.80$

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

38 Views

Kickstart Your Career

Get certified by completing the course

Get Started