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

Solution:

Given, rain water from a roof drains into a cylindrical vessel.

Dimension of roof is 22 m × 20 m

Cylindrical vessel has base diameter 2 m and height 3.5 m

We have to find the rainfall in cm if the rain water collected from the roof just fill the cylindrical vessel.

Volume of cylinder = πr²h

Given, base diameter = 2m

Radius = 1 m

1 m = 100 cm

Radius = 100 cm

h = 3.5 m

= 3.5(100)

h = 350 cm

Volume of rain water collected in a cylindrical vessel to its full capacity = π(100)²(350)

= 3500000π cm³

Volume of rain water collected on the roof = length × width × height

Given, length = 22 m

1 m = 100 cm

So, length = 2200 cm

Width = 20 m = 2000 cm

= 2200 × 2000 × h

= 4400000h cm³

Now, 4400000h = 3500000π

h = 3500000(22/7) / 4400000

= 35(22/7) / 44

= 5(22) / 44

= 5/2

= 2.5 cm

Therefore, the rainfall is 2.5 cm

✦ Try This: The rain water from a roof of dimensions 28 m × 26 m drains into a cylindrical vessel having diameter of base 3 m and height 5.3 m. If the rain water collected from the roof just fill the cylindrical vessel, then find the rainfall in cm.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13

NCERT Exemplar Class 10 Maths Exercise 12.4 Problem 19

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

Summary:

The rain water from a roof of dimensions 22 m × 20 m drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m. If the rain water collected from the roof just fill the cylindrical vessel, then the rainfall is 2.5 cm

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