Question

A cone of slant height 25 cm has a curved surface are 550 cm². Find the height and volume of the cone.

Answer 1

Slant height of the cone = 25 cm
Curved surface area of the = 550 cm²

$$\begin{gathered} \mathrm{i}.\mathrm{e}.,\mathrm{\pi }rl=550 \\ \Rightarrow \frac{22}{7}\times r\times 25=550 \\ \Rightarrow \mathrm{r}=\frac{550\times 7}{22\times 25} \\ \Rightarrow r=7\mathrm{cm} \end{gathered}$$

$$\begin{gathered} \mathrm{Also},h=\sqrt{l^2-r^2} \\ =\sqrt{{25}^2-7^2} \\ =\sqrt{625-49} \\ =\sqrt{576} \\ =24\mathrm{cm} \end{gathered}$$


$$\begin{gathered} \therefore \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cone}=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h} \\ =\frac{1}{3}\times \frac{22}{7}\times 7^2\times 24 \\ =1232{\mathrm{cm}}^3 \end{gathered}$$