The external and the internal radii of a hollow right circular cylinder of height 15 cm are 6.75 cm and 5.25 cm respectively. If it is melted to form a solid cylinder of height half of the original cylinder, then the radius of the solid cylinder is

Solution (By Examveda Team)

$$\eqalign{ & {\text{Volume of cylinder}} = \pi r_1^2h - \pi r_2^2h \cr & = \pi h\left( {r_1^2 - r_2^2} \right) \cr & = \pi h\left( {{r_1} + {r_2}} \right)\left( {{r_1} - {r_2}} \right) \cr & = \frac{{22}}{7} \times 15 \times \left( {6.75 + 5.25} \right)\left( {6.75 - 5.25} \right) \cr & = \frac{{22}}{7} \times 15 \times 12 \times 1.5 \cr & {\text{Volume}} = \pi r_3^2\frac{h}{2} = \frac{{22}}{7} \times 15 \times 12 \times 1.5 \cr & r_3^2 \times \frac{{15}}{2} = 15 \times 12 \times 1.5 \cr & {r_3} = 6 \cr} $$