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Q.

The rainwater from a roof of 40 m $×$ 24 m drains into a cylindrical tank having diameter of base 8 m and height 5.5 m. If the tank is just full, then the height of the rainfall will be ____.

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Detailed Solution

The rainwater from a roof of 40 m

×

24 m drains into a cylindrical tank having diameter of base 8 m and height 5.5 m. If the tank is just full, then the height of the rainfall will be 0.288 m.
Note that,
Length of roof (l)= 40 m
Width of the roof (b)= 24 m
Height of the tank (h)= 5.5m
So, the base radius of the tank,

r = 82 = 4 m

Suppose the height of the rainfall is h.
According to the question,
Volume of rainfall = Volume of cylindrical tank
Volume of a cylindrical tank=

π r 2 h

Where, r is the radius and h is the height of the cylindrical tank.

l b h = π r 2 h

⇒ 40 × 24 × h = 227 × 4 × 4 × 5.5 h = 227 × 4 × 4 × 5.5 40 × 24 ⇒ h = 0.288 m

So, the height of the rainfall is 0.288 m.
Therefore, 0.288 m is the correct answer.

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