Question

The diameter of a cylindrical well is $\mathbf{4}\mathbf{.}\mathbf{5}\mathbf{}\mathit{m}$ and depth of the well is $\mathbf{14}\mathbf{}\mathit{m}$. Find the cost of cementing its inner curved surface at the rate of $\mathbf{12}\mathbf{.}\mathbf{50}$ rupees per square metre.

Answer 1

Step 1. Given measures of the cylindrical well:

Diameter $\left(d\right)$ = $4.5m$

Depth $\left(h\right)$ = $14m$

Step 2. Radius $\left(r\right)$ of the cylindrical well:

Diameter $\left(d\right)$ of the cylindrical well = $4.5m$

Thus, radius $\left(r\right)$ of the cylindrical well = $\frac{4.5}{2}m$ (As $r=\frac{d}{2}$ )

Step 3. The inner curved surface area (C.S.A.) of the cylindrical well:

The curved surface area (C.S.A.) of the cylinder = $2\mathrm{\pi rh}$

Inner curved surface area of the cylindrical well = $2\times \frac{22}{7}\times \frac{4.5}{2}\times 14$ (As $\mathrm{\pi }=\frac{22}{7}$ )

= $22\times 4.5\times 2$

= $198m^2$

Step 4. Cost of cementing inner curved surface of cylindrical well:

Cost of cementing per square meter = $12.50$ Rupees

Cost of cementing $198m^2$ = $12.50\times 198$

= $2475$ Rupees

Hence, the cost of cementing inner curved surface of the cylindrical well at the rate of $12.50$ rupees per square meter is $2475$ rupees.