Question

The volume of a right circular cylinder with its height equal to the radius is $25\frac{1}{7}$ cm³. Find the height of the cylinder.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Height}=\mathrm{Base}\mathrm{radius}\mathrm{i}.\mathrm{e}.h=r \\ \mathrm{As}, \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cylinder}=25\frac{1}{7}{\mathrm{cm}}^3 \\ \Rightarrow \mathrm{\pi }{r}^{2}h=\frac{176}{7} \\ \Rightarrow \frac{22}{7}\times h^2\times h=\frac{176}{7} \\ \Rightarrow h^3=\frac{176\times 7}{7\times 22} \\ \Rightarrow h^3=8 \\ \Rightarrow h=\sqrt[3]{8} \\ \therefore h=2\mathrm{cm} \end{gathered}$$

So, the height of the cylinder is 2 cm.