Question

It costs $Rs2200$ to paint the inner curved surface of a cylindrical vessel $10m$ deep. If the cost of painting is at the rate of $Rs20$per $m^2$, find

(i) inner curved surface area of the vessel

(ii) radius of the base

(iii) capacity of the vessel (Assume $\pi =\frac{22}{7}$)

Answer 1

Step $1:\left(i\right)$ Calculate inner curved surface area of the vessel :

Height of cylinder $\left(h\right)=10m$

Cost of painting for $1m^2=₹20$

Total cost for painting the inner curved surface $=₹2200$

Hence, total inner curved surface area $=\frac{2200}{20}=110m^2$.

Step $2:\left(ii\right)$ Calculate the radius of the base :

Let the base radius $=r$

So as, Lateral surface $=$(circumference of base circle of cylinder) $\times$ height

$$\begin{gathered} \Rightarrow 110=\left(2\pi r\right)\times h \\ \Rightarrow 110=2\times \frac{22}{7}\times r\times 10 \\ \Rightarrow r=\frac{110\times 7}{2\times 22\times 10} \\ \Rightarrow r=1.75cm \end{gathered}$$

Hence, the radius of the base is $1.75cm$.

Step $3:\left(iii\right)$ Calculate the capacity of the vessel :

Volume of cylinder $=\left(\pi r^{2}h\right)$

$$\begin{gathered} =\frac{22}{7}\times \frac{7}{4}\times \frac{7}{4}\times 10 \\ =96.25c{m}^3 \end{gathered}$$

Hence, the capacity of the vessel is $96.25c{m}^3$.