Question

Question 5 (iii)
It costs Rs. 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of $Rs20per{m}^2$, find:

(iii) Capacity of the vessel

$[Assume\pi =\frac{22}{7}]$

Answer 1

(iii)

Rs. 20 is the cost of painting $1m^2$ area.

Area painted for Rs. 2200 $=(\frac{1}{20}\times 2200)m^2$

$=110m^2$

Therefore, the inner surface area of the vessel is $110m^2$.

Let the radius of the base of the vessel be r.

Height (h) of the vessel = 10 m
Surface area $=2\pi rh=110m^2$

$\Rightarrow (2\times \frac{22}{7}\times r\times 10)m=110m^2$
$\Rightarrow r=\left(\frac{7}{4}m\right)=1.75m$

Volume of the vessel $=\pi r^{2}h$

$=[\frac{22}{7}\times (1.75{)}^2\times 10]m^3=96.25m^3$

Therefore, the capacity of the vessel is 96.25 $m^3$ or 96250 litres.