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Question
Two cylinders A and B are formed by folding a rectangular sheet of dimensions 20 cm × 10 cm along its length and also along its breadth respectively. Then volume of A is ______ of volume of B.
Solution
Two cylinders A and B are formed by folding a rectangular sheet of dimensions 20 cm × 10 cm along its length and also along its breadth respectively. Then volume of A is twice of volume of B
Explanation:
We have, a rectangular sheet of dimensions 20 cm × 10 cm.
If we fold it along its length, which is 20 cm, then the resultant figure is a cylinder with height, h = 10 cm and base circumference, 2πr = 20 cm
⇒ `r = 20/(2pi) = 10/pi cm`
∴ The volume of the cylinder, so formed = πr2h
= `pi xx 10/pi xx 10/pi xx 10`
= `1000/pi cm^3`
= V1 (say) ...(i)
Again, if we fold the rectangular sheet along its breadth, which is 10 cm, the figure so obtained is a cylinder with height h = 20 cm and the base circumference 2πr = 10 cm
⇒ `r = 10/(2pi) = 5/pi cm`
∴ Volume of the cylinder = πr2h
= `pi xx 5/pi xx 5/pi xx 20`
= `500/pi cm^3`
= V2 (say) ...(ii)
i.e. V2 = 2V1
From equations, (i) and (ii), we see that the volume of A is twice the volume of B.
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