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The rain which falls on a roof $18 m$ long and $16.5 m$ wide is allowed to be stored in a cylindrical tank $8 m$ in diameter. If it rains $10 cm$ on a day, what is the rise of water level in the tank due to it?

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59.06 cm

45.89 cm

34.76 cm

24.56 cm

answer is A.

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Detailed Solution

It is given rainfall of length 18 m, width 16.5 m and a cylindrical tank of diameter 8 m.
We know,1 m = 100

cm

Height of water on the roof = 10

cm

⇒

Height of water on the roof =0.1 m
Since, radius =

D i a m e t e r 2

So, radius (r) is,

r = 82 ⇒ r = 4 m

Volume of water collected =

l × b × h

⇒

Volume of water collected

= 18 × 16.5 × 0.1

⇒

Volume of water collected = 29.7

m 3

Let

h

be the height of the water in the tank.
The volume of water rose up = Volume of water collected = 29.7

m 3

Since, volume of water rose up =

π r 2 h

Height (h) =

V o l u m e π r 2

⇒ h = 29.7 227 × 42

⇒ h = 29.7 × 7 22 × 4 × 4

⇒ h

= 0.5906 m

⇒ h

=59.06cm (1m=100cm)
Therefore, the rise of water level in the tank due to rain is 59.06

cm

.
Hence option (1) is correct.

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