# ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.5 in Chapter 17 - Mensuration

Question 6 Mensuration Exercise 17.5

The rain water from a roof of dimensions 22 m x 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:

Although the water is transferred from cuboidal roof to cylindrical vessel, its volume remains the same.

Given dimensions of the roof = 22 m × 20 m

Let the rainfall be x cm.

Volume of water = (22×20×x)m3

Diameter of the cylindrical base = 2 m

So radius of the cylindrical base = 2/2 = 1 m

Height of the cylindrical base, h = 3.5 m

Volume of cylindrical vessel =π r2h

= (22/7)×12×3.5

= 11 m3

Since the rain water collected from the roof just fill the cylindrical vessel, the volumes are equal.

22×20×x = 11

x = 11/22×20

= 1/40 m

= (1/40)×100 cm

= 2.5 cm

Hence the rainfall is 2.5 cm.

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