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