Question

Find the volume, curved surface area and the total surface area of a cone whose height and slant height are 6 cm and 10 cm respectively.

Answer 1

Height of the cone, h = 6 cm
Slant height of the cone, l = 10 cm
Radius, r = $\sqrt{l^2-h^2}=\sqrt{100-36}=\sqrt{64}=8\mathrm{cm}$

Volume of the cone = $\mathrm{\pi }{r}^{\mathit{2}}h\mathit{}$
$$\begin{gathered} =\frac{1}{3}\times 3.14\times 8^2\times 6 \\ =401.92{\mathrm{cm}}^3 \end{gathered}$$

Curved surface area of the cone = $\mathrm{\pi r}l$
$$\begin{gathered} =3.14\times 8\times 10 \\ =251.2{\mathrm{cm}}^2 \end{gathered}$$

∴ Total surface area = $\mathrm{\pi }rl+\mathrm{\pi }{r}^2$
$$\begin{gathered} =251.2+3.14\times 8^2 \\ =452.16{\mathrm{cm}}^2 \end{gathered}$$