Question

The capacity of a cylindrical cistern at a petrol pump is 38,500 litres. If its diameter is 3.5 m, find its height.

Answer 1

Let the height be h.

Then,

${ \huge{{\pi {r}^{2} h = 38500 \: l}}}$

We Know,

${ \huge{ \mathbf{1 \: litre = \frac{1}{1000} \: {m}^{3} }}}$

Therefore,

${ \huge{ \mathtt{\pi {r}^{2} h = 38500 \times \frac{1}{1000} }}} \\ \\ { \huge{ \mathtt{ \: \: \: \: \: \: \: h = \frac{38.5}{ \frac{22}{7} \times {( \frac{3.5}{2} )}^{2} } }}} \\ \\ { \huge{ \mathtt{ \: \: \: \: \: \: \: h = \frac{ 38.5 }{ \frac{22}{7} \times \frac{12.25}{4} } }}} \\ \\ { \huge{ \mathtt{ \: \: \: \: \: \: \: h = \frac{38.5 \times 7 \times 4}{22 \times 12.25} }}} \\ \\ { \huge{ \mathtt{ \: \: \: \: \: \: \: h = \frac{385 \times 28}{22 \times 122.5} }}} \\ \\ { \huge{ \mathtt{ \: \: \: \: \: \: \: h = \frac{10780}{2695} }}} \\ \\ { \huge{ \mathtt{ \: \: \: \: \: \: \: { \red{ \boxed{h =4 \: m}}} }}}$

Answer 2

Answer:

Height of cylindrical cistern is ≈ 4 m

Step-by-step explanation:

Volume of Cylinder

$\boxed{V = \pi {r}^{2} h}$

Volume in liters = 38500

Volume in meter-cube

$= \frac{38500}{1000} \\ \\ = 38.5 \: {m}^{3}$

Diameter =3.5

Radius = 1.75 m

$38.5 = \pi( {1.75)}^{2} h \\ \\ h = \frac{38.5}{\pi \times 1.75 \times 1.75} \\ \\ h = \frac{38.5 \times 7}{22 \times 1.75 \times 1.75} \\ \\ = \frac{269.5}{67.38} \\ \\h = 3.9997 \\ \\ h = 4 \: m$

Height of cylindrical cistern is approx 4 m