Question

The volume of a cone of height 5 cm is 753.6 cm³. This cone and a cylinder have equal radii and height. Find the total surface area of cylinder. (Given $\mathrm{\pi }=3.14$)

Answer 1

Given:
Height of the cone = 5 cm
Volume of the cone = 753.6 cm³
$$\begin{gathered} \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ \frac{1}{3}\mathrm{\pi }{r}^{2}h\mathit{=}753.6 \\ \Rightarrow r^2=\frac{753.6\times 3}{5\times 3.14} \\ \Rightarrow r^2\mathit{=}144 \\ \Rightarrow r^2\mathit{=}144 \\ \Rightarrow r\mathit{}=\mathit{}\sqrt{\mathit{144}} \\ \Rightarrow r\mathit{}=12\mathrm{cm} \end{gathered}$$

It is given that the radius and height of the cone and cylinder are equal.
Thus, we have:
Height of the cylinder = 5 cm
Radius of the cylinder = 12 cm
Total surface area = 2$\mathrm{\pi }$r(h + r)
= 2 × 3.14 × 12 × (5 + 12)
= 1281.12 cm²