Question

Two cylinders A and B are formed by folding a rectangular sheet of dimensions $20cm\times 10cm$ along its length and also along its breadth respectively. Then, volume of A is ___ of volume of B.

Answer 1

Answer: Then, volume of A is twice of volume of B.

We have, a rectangular sheet of dimensions $20cm\times 10cm$

If we fold it along its length, which is $20cm$, then, the resultant figure is a cylinder with height, $h=10cm$ and base circumference, $2\pi r=20cm$

$\Rightarrow r=\frac{20}{2\pi }=\frac{10}{\pi }cm$

$\therefore$ The volume of the cylinder, so formed $=\pi r^{2}h$

$=\pi \times \frac{10}{\pi }\times \frac{10}{\pi }\times 10$

$=\frac{1000}{\pi }c{m}^3$

$=V_1$ (say) ...... (i)

Again if we fold the rectangular sheet along its breadth, which is $10cm$, the figure so obtained is a cylinder with height, $h=20cm$ and the base circumference $2\pi r=10cm$

$\Rightarrow r=\frac{10}{2\pi }=\frac{5}{\pi }cm$

$\therefore$ Volume of the cylinder $=\pi r^{2}h=\pi \times \frac{5}{\pi }\times \frac{5}{\pi }\times 20$

$=\frac{500}{\pi }c{m}^3$

$=V_2$ (say)...(ii)

From Eqs. (i) and (ii), we see that the volume of A is twice the volume of B i.e. $V_1=2V_2$.