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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 $=Rs.\ \frac{44 \times 8.7 \times 10}{10}$
$=Rs.\ 382.80$
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