Question

The rain water from a roof of dimensions 22m x 10m drains into a cylindrical vessel having diameter of base 2m and​

Answer 1

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Correction in the given question:-

The rain water from a roof of 22m×20m drains into a cylindrical vessel having diameter of base 2m and height 3.5m. If the vessel is just full, find the rainfall in cm.

Solution:-

We have,

Radius of cylindrical vessel = r = 1m

Height of cylindrical vessel h = 3.5m

Volume of cylindrical vessel = $πr{^2}$h = $\frac{22}{7}$×$1{^2}$×$3.5m{^3}$ = $11m{^3}$

let the rainfall be x cm.

Then volume of water = Volume of a cuboid of base 22m × 20m and height x metres = (22 × 20 × x) $m{^3}$

Since the vessel is just full of water that drains out of the roof into the vessel

Volume of the water = Volume of the cylindrical vessel

22 × 20 × x = 11

=> x = $\frac{11}{22×20}$ = 0.025m = 2.5m

Answer => Rainfall = 2.5m

Answer 2

We have,

Radius of cylindrical vessel = r = 1m

Height of cylindrical vessel h = 3.5m

Volume of cylindrical vessel = πr${^2}$ h = $\frac{22}{7}$ × 1${^2}$3.5m${^3}$ = 11m${^3}$

let the rainfall be x cm.

Then volume of water = Volume of a cuboid of base 22m × 20m and height x metres = (22 × 20 × x) m${^3}$

Since the vessel is just full of water that drains out of the roof into the vessel

Volume of the water = Volume of the cylindrical vessel

22 × 20 × x = 11

=> x = $\frac{11}{22×20}$ = 0.025m = 2.5m

Answer => Rainfall = 2.5m