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. The volume of A is ________ the volume of B.

• A. equal to
• B. one fourth of
• C. double
• D. half of

Answer 1

The correct option is C double

If we fold the rectangular sheet along its length, which is 20 cm, then the resultant figure is a cylinder with height h is 10 cm and base circumference $S=2\pi r=20cm$
The volume of a cylinder having radius r and height h
$=\pi r^{2}h=\frac{4\pi \times \pi r^{2}h}{4\pi }$
$=\frac{4{\pi }^2{r}^{2}h}{4\pi }$
$=\frac{S^{2}h}{4\pi }$

The volume of cylinder A $=\frac{{20}^2\times 10}{4\pi }c{m}^2$

When we fold the rectangular sheet along its breadth, which is 10 cm, then the resultant figure is a cylinder with height h is 20 cm and base circumference $S=2\pi r=10cm$
Similarly, the volume of cylinder B $=\frac{{10}^2\times 20}{4\pi }c{m}^2$
So, the ratio of the volume of cylinder A to the volume of cylinder B $=\frac{({20}^2\times 10)}{({10}^2\times 20)}=2:1$