# ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.1 in Chapter 17 - Mensuration

Question 22 Mensuration Exercise 17.1

A rectangular sheet of tin foil of size 30 cm × 18 cm can be rolled to form a cylinder in two ways along length and along breadth. Find the ratio of volumes of the two cylinders thus formed.

Solution:

The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it.

Given size of the sheet = 30 cm×18 cm

If we roll it lengthwise, base circumference,

2π r = 30

2×(22/7)r = 30

r = 30×7/2×22 = 210/44 = 105/22 cm

Height, h = 18 cm

Volume of the cylinder, V1 = π r2h

= (22/7)×(105/22)2×18

= 15×105×9/11

If we roll it breadthwise, base circumference, 2π r = 18

2×(22/7)r = 18

r = 18×7/2×22 = 126/44 = 63/22 cm

Height, h = 30 cm

Volume of the cylinder, V2 = π r2h

= (22/7)×(63/22)2×30

= 9×63×15/11

V1/V2 = (15×105×9/11)÷( 9×63×15/11)

= (15×105×9/11)×(11/9×63×15)

= 105/63

= 15/9

= 5/3

Ratio of the volumes of two cylinders is 5:3.

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