Question

The cost of painting the curved surface area of a cylindrical container of depth 5 inch is $\$8800$. If the painter charges $\$40$ per sq inch to paint the cylindrical container, then find its radius.
$[\text{Take}\pi =\frac{22}{7}]$

Answer 1

Cost of painting the curved surface area = $\$8800$
Cost of painting per sq inch
= $\$40$

∴ Area of cylinder that was painted
$=\frac{8800}{40}=220\text{sq inch}$


So, curved surface area of the cylinder = 220 sq inch

We know,
Curved surface area of cylinder
$=2\pi rh$

$\text{Height of cylinder}=5\text{inch}$

So, putting values we get:
$\Rightarrow 2\times \frac{22}{7}\times r\times 5=220$

$\Rightarrow r=\frac{220\times 7}{2\times 22\times 5}$

$\Rightarrow r=\frac{10\text{/}220\times 7}{2\times \text{/}22\times 5}=\frac{5\text{/}10\times 7}{\text{/}2\times 5}$

$\Rightarrow r=7\text{inch}$

Hence, radius of the cylinder = 7 inch.