Question

Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape formed.

Answer 1

Radius, r = 8 cm
Height, h = 15 cm
$$\begin{gathered} l=\sqrt{h^2+r^2} \\ l=\sqrt{{15}^2+8^2} \\ l=\sqrt{225+64} \\ l=\sqrt{289}=17cm \end{gathered}$$
When the two cones are joined through their bases so, the total surface area of the shape formed will be sum of the curved surface areas
of the two cones.
Curved surface area of the cone
$$\begin{gathered} CSA=\mathrm{\pi rl} \\ =\mathrm{\pi }\left(8\right)\left(17\right) \\ =427.4{\mathrm{cm}}^2 \end{gathered}$$
similarly curved surface area of the other cone will also be the same.
Hence, the total surface area of the solid formed = 427.4 + 427.4 = 854.8 cm²