The difference between the outer and inner radii of a hollow right circular cylinder of length $\displaystyle 14$ cm is $\displaystyle 1$ cm. If the volume of the metal used in making the cylinder is $\displaystyle 176 \mathrm{~cm}^{3}$, find the outer and inner radii of the cylinder.

Let outer radius be \(\displaystyle \mathrm{r}_{2} \mathrm{~cm}\) and inner radius be \(\displaystyle \mathrm{r}_{1} \mathrm{~cm}\). \[\therefore r_{2}-r_{1}=1 \] Volume of metal used \(\displaystyle =176 \mathrm{~cm}^{3}\) \[\Rightarrow \frac{22}{7} \times 14 \times\left(\mathrm{r}_{2}^{2}-\mathrm{r}_{1}^{2}\right)=176 \] \[\Rightarrow \mathrm{r}_{2}+\mathrm{r}_{1}=4 \] Solving (i) and (ii), we get \[r_{2}=\frac{5}{2} \text { or } 2.5, r_{1}=\frac{3}{2} \text { or } 1.5 \] Therefore, outer radius \(\displaystyle =2.5 \mathrm{~cm}\) and inner radius \(\displaystyle =1.5 \mathrm{~cm}\)