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$2 cm$ rain has fallen on a square kilometer of land. Assuming that $50 %$ of the rain drops could have been collected and contained in a pool having a $100 m × 10 m$ base, by what level would the water level in the pool have increased?

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20 m

10 m

25 m

30 m

answer is B.

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Detailed Solution

The area of the land is,

⇒ A = 1 km 2 ⇒ A ​ = 1000 m 2

The height of the fallen rain on the land is,

⇒ h = 2 c m = 0.02 m

The area of the pool base is,

⇒ A p = 100 m × 10 m ⇒ A p = 1000 m 2

The total volume of the rain falling on the land is given by

⇒ V = The area of the land × The height of the fallen rain on the land ​ ⇒ V = A × h

Substituting the values,

⇒ V = 10002 m 2 × 0.02 m V = 20000 m 3

Now according to the question

50 %

of the total volume of rain is collected and contained in the pool, so
The volume of the rain water collected in the pool is,

⇒ V p = 0.5 × V

Substituting the values and we get,

⇒ V p = 0.5 × 20000 m 3 ​ ⇒ V p = 10000 m 3

Let us suppose the level of the water in the pool be

h p

then,

⇒ The increase in the level of water in the pool = The volume of the rain water collected in the pool The area of pool base

⇒ h p = V p A p

Substitute the values,

⇒ h p = 10000 m 3 1000 m 2 ⇒ h p = 10 m

Therefore, the increase in the water level in the pool is

10 m

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