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.

Answer 1

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.