the rainwater from a 22m 20m roof drains into a cylindrical vessel od diameter 2m and height 3.5m. if the rainwater collected from the roof fills 4/5th of the cylindrical vessel then find the rainfall in centimetre.
Answers
Answer:
Here, in the question problem, area of the roof from where the rain water is collected = 22m × 20m.
But, instead of storing in that area, it is made to flow into a cylindrical vessel of base area (given by π × r^2, where r = diameter/2) = π × (2m/2)^2, where it stood up to to a height of 3.5m. on storing.
We need to find the height of the water body which is now contained in the cylindrical vessel would be if it is made to spread over an area equal to that of the roof.
So, (Area of the roof ÷ Base area of the cylindrical container) = (Height of water in the cylindrical container ÷ Height of water level on the roof if it is allowed to stand there ( let it be x)).
That is, [(22m × 20m) ÷ (π × 1m^2)] = (3.5m ÷ x).
That is, x = (3.5 × π)m^2 ÷ (22 × 20)m.
That is, x = (3.5 × 22)m ÷ (22 × 20 × 7) since π = 22/7.
That is, x = (1/40)met.
But, we are told to mention it in cm.
So, (1/40)m = (100/40)cm. = 2.5cm. (ANS).