Question

A cylindrical vessel open at the top has a base diameter of 56 cm. If the total cost of painting the outer curved surface of the vessel is Rs 352 at the rate of Rs 0.2 per $100{cm}^2,$ then the height of the vessel is

• A. $15m$
• B. $10m$
• C. $6m$
• D. $12m$

Answer 1

The correct option is B $10m$

$\Rightarrow$ Diameter $\left(d\right)=56cm$

$\Rightarrow$ Radius $\left(r\right)=\frac{d}{2}=\frac{56}{2}-28cm$

As rate is $Rs.0.2$ per $100c{m}^2$

$\Rightarrow$ Cost of painting $=Rs.0.002$

$\Rightarrow$ Total cost of painting $=Rs.352$

Total cost of painting $=$ Outer curved surface area of vessel $\times$ Cost of painting.

$\Rightarrow$ $352=2\pi rh\times 0.002$

$\Rightarrow$ $352=2\times \frac{22}{7}\times 28\times h\times 0.002$

$\Rightarrow$ $352=44\times 4\times h\times 0.002$

$\Rightarrow$ $352=176\times 0.002\times h$

$\Rightarrow$ $h=\frac{352}{176\times 0.002}$

$\Rightarrow$ $h=\frac{352\times 1000}{176\times 2}$

$\Rightarrow$ $h=1000cm$

$\therefore$ $h=10m$