Question

Find the volume, curved surface area and the total surface area of a cone having base radius 35 cm and height 84 cm.

Answer 1

Here, h = 84 cm and r = 35 cm
Volume of the cone = $\frac{1}{3}\mathrm{\pi }{r}^{2}h$
$$\begin{gathered} =\frac{1}{3}\times \frac{22}{7}\times {35}^2\times 84{\mathrm{cm}}^3 \\ =22\times 5\times 35\times 28 \\ =107800{\mathrm{cm}}^3 \end{gathered}$$

Also, l = $\sqrt{h^2+r^2}=\sqrt{{35}^2+{84}^2}=\sqrt{1225+7056}=\sqrt{8281}=91\mathrm{cm}$

Curved surface area = $\mathrm{\pi }rl$
$$\begin{gathered} =\frac{22}{7}\times 35\times 91{\mathrm{cm}}^2 \\ =10010{\mathrm{cm}}^2 \end{gathered}$$

∴ Total surface area = $(\mathrm{\pi }rl+\mathrm{\pi }{r}^2)\mathrm{sq}\mathrm{units}$
$$\begin{gathered} =10010+\frac{22}{7}\times {35}^2 \\ =10010+3850 \\ =13860{\mathrm{cm}}^2 \end{gathered}$$