Question

It costs $2200$ Rs to point 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) the radius of the base.
(iii) the capacity of the vessel.

Answer 1

Curved Surface Area$=\frac{cost}{Rate}=\frac{2200}{20}=110m^2$

$2\pi rh=110m^2$ where $r$ is the radius of the base.

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

$\Rightarrow r=\frac{110\times 7}{10\times 2\times 22}=\frac{7}{4}m=175cm$

Capacity of the vessel,

$v=\pi r^{2}h=\frac{22}{7}\times \frac{7}{4}\times \frac{7}{4}\times 10$

$=96.25m^3$.