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Q.

Water is flowing at the rate of 15km/hour through a pipe of diameter 14cm into a cuboidal pond which is 50m long and 44m wide. In what time will the level of water in the pond rise by 21cm?


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a

3 hrs.

b

2 hrs.

c

4 hrs.

d

5 hrs. 

answer is B.

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Detailed Solution

We know that, the space occupied by an object/ solid body is called the volume of the particular object/ solid body.
We measure volume in the cubic unit.
The formula of Volume of Cuboid = l×b×h and,
Area of circle = πr².
Given that, speed of flow of water = 15 km/hour = 15 × 1000 m/h = 15000 m/hr (since, 1 km = 1000 m).
So, length of water in 1 hr = 15000 m.
Also, given diameter of pipe, d = 14 cm,
length of pond, l = 50 m,
width of pond, b = 44 m, and
height of water in pond h = 21 cm.
Question Image Volume of water in the cuboidal pond, V = l×b×h.
Substitute the values l, b and h. We get,
V=50×44× 21 100 1 cm= 1 100  m V=44× 21 2  V=22×21   Volume of water in the cuboidal pond, V = 462 m³.
Let us convert diameter into radius.
Radius of pipe, r = d 2 r= 14 2 r=7 cm r= 7 100 1 cm= 1 100  m r=0.07 m   Radius of pipe, r = 0.07 m.
Area of the pipe which is in the form of a circle, A = πr².
A=π× (0.07) 2 A=0.0049π A=0.0049× 22 7 A=0.0007×22 A=0.0154  m 2   Area of the pipe, A = 0.0154 m²
Now, let us find the requires time.
Required time =  Volume of water in the cuboidal pond  ( Area of pipe × Length of water in 1 h) = 462  m 3 0.0154  m 2 ×15000 m = 462 231 =2 hours    Hence, the level of water in the pond will rise by 21cm in 2 h.
The correct option is (2).
 
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