Question

The rain water from a 22 m × 20 m roof drains into a cylindrical vessel of diameter 2 m and height 3.5 m. If the rain water collected from the roof fills `4/5`th of the cylindrical vessel, then find the rainfall in centimetre. 

Answer 1

We have,

The lenghth of the roof, l = 22 m,

The width of the roof, b = 20 "m"

The base radius of the cylindrical vessel, `"R" = 2/2 =1  "m"`

The height of the cylindrical vessel, H = 3.5 m

Let the height of the rainfall be h.

Now,

Volume of rainfall = Volume of rain water collected in the cylindrical vessel

`rArr "lbh" = 4/5xx "Volume of cylindrical vessel"`

`rArr 22xx 20xxh =4/5xxpi"R"^2"H"`

`rArr 440"h" = 4/5 xx 22/7xx1xx1xx3.5`

`rArr "h" = 4/5xx22/7xx3.5/440`

`rArr "h" = 0.02  "m"`

∴ h =2 cm

So, the height of the rainfall is 2 cm.