Question

In a hospital used water is collected in a cylindrical tank of diameter 2 m and height 5 m. After recycling, this water is used to irrigate a park of hospital whose length is 25 m and breadth is 20 m. If tank is filled completely then what will be the height of standing water used for irrigating the park.

Answer 1

Diameter of cylinder (d) = 2 m
Radius of cylinder (r) = 1 m
Height of cylinder (H) = 5 m
Volume of cylinderical tank, V_c = $\mathrm{\pi }{r}^{2}H$ = $\mathrm{\pi }\times {\left(1\right)}^2\times 5=5\mathrm{\pi }\mathrm{m}$

Length of the park (l) = 25 m
Breadth of park (b) = 20 m
height of standing water in the park = h​
Volume of water in the park = lbh = $25\times 20\times h$

Now water from the tank is used to irrigate the park. So,
Volume of cylinderical tank = Volume of water in the park

$$\begin{gathered} \Rightarrow 5\mathrm{\pi }=25\times 20\times h \\ \Rightarrow \frac{5\mathrm{\pi }}{25\times 20}=h \\ \Rightarrow h=\frac{\mathrm{\pi }}{100}\mathrm{m} \\ \Rightarrow h=0.0314\mathrm{m} \end{gathered}$$