Two rectangular sheets of paper, each 30 cm × 18 cm are made into two right circular cylinders, one by rolling the paper along its length and the other along the breadth. The ratio of the volumes of the two cylinders, thus formed, is :

Solution(By Examveda Team)

Clearly, the cylinder formed by rolling the paper along its length has height 18 cm and circumference of base 30 cm i.e.,
$$\eqalign{ & h = 18{\text{ cm and }} \cr & {\text{2}}\pi r = 30 \cr & Or,r = \frac{{30}}{2} \times \frac{7}{{22}} \cr & Or,r = \frac{{105}}{{22}} \cr} $$
∴ Volume :
$$\eqalign{ & = \pi {r^2}h \cr & = \left( {\frac{{22}}{7} \times \frac{{105}}{{22}} \times \frac{{105}}{{22}} \times 18} \right){\text{ c}}{{\text{m}}^3} \cr & = \frac{{14175}}{{11}}{\text{ c}}{{\text{m}}^3} \cr} $$
The cylinder formed by rolling the paper along its breadth has height 30 cm and circumference of base 18 cm i.e.,
$$\eqalign{ & h = 30{\text{ cm and }} \cr & {\text{2}}\pi r = 18 \cr & Or,r = \frac{{18}}{2} \times \frac{7}{{22}} \cr & Or,r = \frac{{63}}{{22}} \cr} $$
∴ Volume :
$$\eqalign{ & = \pi {r^2}h \cr & = \left( {\frac{{22}}{7} \times \frac{{63}}{{22}} \times \frac{{63}}{{22}} \times 30} \right){\text{ c}}{{\text{m}}^3} \cr & = \frac{{8505}}{{11}}{\text{ c}}{{\text{m}}^3} \cr} $$
Required ratio :
$$\eqalign{ & = \frac{{14175}}{{11}}:\frac{{8505}}{{11}} \cr & = 5:3 \cr} $$