Question

Question 47

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

Twice
We have, a rectangular sheet of dimensions $20cm\times 10cm$
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, $2\pi r=20cm$

$\Rightarrow r=\frac{20}{2\pi }=\frac{10}{\pi }cm$
$\therefore$ 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 10 cm, the figure so obtained is a cylinder with height, h = 20 cm 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)
i.e. $V_2=2V_1$
From Eqs. (i) and (ii), we see that the volume of A is twice the volume of B.