Question

If the area of the base of a right circular cone is 3850 cm² and its height is 84 cm, then find the slant height of the cone.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Height}=84\mathrm{cm} \\ \mathrm{Let}\mathrm{the}\mathrm{radius}\mathrm{and}\mathrm{the}\mathrm{slant}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{cone}\mathrm{be}r\mathrm{and}l,\mathrm{respectively}. \\ \mathrm{As}, \\ \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{base}\mathrm{of}\mathrm{the}\mathrm{cone}=3850{\mathrm{cm}}^2 \\ \Rightarrow \mathrm{\pi }{r}^2=3850 \\ \Rightarrow \frac{22}{7}\times r^2=3850 \\ \Rightarrow r^2=3850\times \frac{7}{22} \\ \Rightarrow r^2=1225 \\ \Rightarrow r=\sqrt{1225} \\ \therefore r=35\mathrm{cm} \\ \mathrm{Now}, \\ l=\sqrt{h^2+r^2} \\ =\sqrt{{84}^2+{35}^2} \\ =\sqrt{7056+1225} \\ =\sqrt{8281} \\ =91\mathrm{cm} \end{gathered}$$

So, the slant height of the given cone is 91 cm.