Question

If costs $2200$ to paint the inner curved surface of a cylindrical vessel $10$ m deep. If the cost of painting is at the rate of $20$ per m${}^2$, find
(i) inner curved surface area of the vessel,
(ii) radius of the base and
(iii) capacity of the vessel.

Answer 1

(i) Cost of painting $1$m${}^2$ area $=$Rs.$20$

$\Rightarrow$Rs.$20$ is cost painting $1$ m${}^2$ area

$\Rightarrow$Rs.$2200$ is cost of painting $=\frac{2200}{20}{m}^2$

$=110$m${}^2$ area

(ii) Let radius $=r_1$, $h=10$m, SA$=2\pi rh=110$

$\Rightarrow$$r=\frac{110\times 7}{22\times 2\times 10}=\frac{7}{4}=1.75$m

(iii) Volume of vessel

$=\pi r^{2}h=\frac{22}{7}\times 1.75\times 1.75\times 10$

$=96.25$m${}^3$

$=96250$ litres