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A Rectangular Sheet of Paper 30 Cm × 18 Cm Can Be Transformed into the Curved Surface of a Right Circular Cylinder in Two Ways I.E., - Mathematics

Sum

A rectangular sheet of paper 30 cm × 18 cm can be transformed into the curved surface of a right circular cylinder in two ways i.e., either by rolling the paper along its length or by rolling it along its breadth. Find the ratio of the volumes of the two cylinders thus formed.

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Solution

Case 1:
Height = h cm = 30 cm
Diameter = d cm = 18 cm
Radius = r cm = 9 cm
∴ Volume = (πr2h) or (π(9 )2(30 )) = 2430π cm3

Case 2:
Height = h cm = 18 cm
Diameter = d cm = 30 cm,
Radius = r cm = 15 cm
∴ Volume = (πr2h) or (π(15 )2(18 )) = 4050π cm3

Hence, the ratio of the volumes of the two cylinders formed is 3:5.

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APPEARS IN

RD Sharma Class 8 Maths
Chapter 22 Mensuration - III (Surface Area and Volume of a Right Circular Cylinder)
Exercise 22.2 | Q 24 | Page 26
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