Question

It costs Rs 3300 to paint the inner curved surface of a cylindrical vessel 10 m deep at the rate of Rs 30 per $m^2$.Find the

(i) inner curved surface area of the vessel,

(ii) inner radius of the base, and

(iii) capacity of the vessel.

Answer 1

Cost of painting $1m^2$= Rs 30.
Cost of painting inner curved surface(I.C.S) area= Rs 3300.
(i) I.C.Surf. $area\times 30=3300$
I.C.Surf.area= 3300/30
I.C.Surf.area= 110$m^2$
(ii) height = 10 m
C.Surf.area of cylinder $110m^2=2\pi rh$
$110m^2=(2\times \frac{22}{7}\times r\times 10)$
$=\frac{440r}{7}$
$\Rightarrow r=\frac{770}{440}$
$\therefore r=1.75m$
(iii) Capacity = volume of well = $\pi .r^2.h$
volume= $\frac{22}{7}\times (1.75\times 1.75)\times 10$
volume=$\frac{673.75}{7}$
volume= 96.25 $m^3$.