Question

Water flows out through a circular pipe whose internal diameter is 2 cm. at the rate of 6 metres per second into a cylindrical tank. The radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes?​

Answer 1

Given :-

• Water flows out through a circular pipe whose internal diameter is 2 cm. at the rate of 6 metres per second into a cylindrical tank.

• The radius of cylinderical tank is 60 cm.

To Find :-

• The rise in the level of water in 30 minutes?

Formula Used :-

$\rm :\longmapsto\:Volume_{(cylinder)} = \pi \: {r}^{2} \: h$

Where,

• r = radius of cylinder

• h = height of cylinder

Solution :-

Given that,

• Diameter of cylindrical pipe, d = 2 cm

• Radius of cylindrical pipe, r = 1 cm

• Water flows from it at the rate of 6 m/ sec = 600 cm/sec

So,

☆ Volume of water flow in 1 second is

$\rm :\longmapsto\:Volume_{(water \: flow \: in \: 1 \: sec)} = \pi \: {r}^{2} \: h$

$\rm :\longmapsto\:Volume_{(water \: flow \: in \: 1 \: sec)} = \pi \: {(1)}^{2} \: (600)$

$\rm :\longmapsto\:Volume_{(water \: flow \: in \: 1 \: sec)} = 600\pi \: {cm}^{3}$

Now,

We know,

$\rm :\longmapsto\:1 \: minute \: = \: 60 \: seconds$

So,

$\rm :\longmapsto\:30 \: minute \: = \: 1800 \: seconds$

Hence,

☆ Volume flow in 1800 seconds is

$\rm :\longmapsto\:Volume_{(water \: flow \: in \: 1800 \: sec)} = 1080000\pi \: {cm}^{3}$

Now,

Let assume that

• The water level rise in tank in 1800 seconds be 'h' cm.

• Radius of cylindrical tank, R = 60 cm

According to statement,

$\rm :\longmapsto\:1080000\pi = \pi {(60)}^{2}h$

$\rm :\longmapsto\:1080000\pi = \pi \times 3600 \times h$

$\rm :\longmapsto\:h = \dfrac{1080000\pi}{3600\pi}$

$\bf\implies \:h = 300 \: cm = 3 \: m$

More Information:

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²