Question

Find the height of a cylindrical tank having radius 3 m to supply 1413 litres of water to each of 60 houses of a society ? (π = 3.14)

Answer 1

Let the height be h.

Then,

${ \large{ \boxed{ \mathbf{Volume = \pi {r}^{2} h = 1413 \: l}}}}$

We Know,

${ \huge{ \boxed{{ \blue{1 \: l = \frac{1}{1000} \: {m}^{3} }}}}}$

Therefore,

${ \huge{ \mathtt{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \pi {r}^{2}h =( 1413 \times 60 \times \frac{1}{1000}) \: {m}^{3} }}} \\ \\ { \huge{ \mathtt{3.14 {(3)}^{2} \times h = \frac{1413 \times 60}{1000} \: {m}^{3} }}} \\ \\ { \huge{ \mathtt{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: h = \frac{1413 \times 60}{1000 \times 3.14 \times {(3)}^{2} } }}} \\ \\ { \huge{ \mathtt{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: h = \frac{1413 \times 60\times 100}{1000 \times 314 \times 9} }}} \\ \\ { \huge{ \mathtt{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: h = \frac{1413 \times 60}{10 \times 2826} }}} \\ \\ { \huge{ \mathtt{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: h = \frac{1413 \times 6}{2826} }}} \\ \\ { \huge{ \mathtt{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: h = \frac{8478}{2826} }}} \\ \\ { \huge{ \mathtt{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { \red{ \boxed{h = 3 \: m}}}}}}$