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

Answer: Option A

Solution

Answer: Option A

Solution:

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