Question

In the figure, from the top of a solid cone of height $12cm$ and base radius $6cm$, a cone of height $4cm$ is removed by a plane parallel to the base. Find the total surface area of the remaining solid. (Use $\pi =22/7$ and $\sqrt{5}=2.236$)

Answer 1

$△OAB\sim △OCD$ [By AA similarity]

$\frac{OA}{OC}=\frac{AB}{CD}$

$AB=\frac{4\times 6}{12}$

$=2cm$

TSA of frustum $=\pi (R_1+R_2)l+\pi (R_1^2+R_2^2)$

$=\pi [(R_1+R_2)\sqrt{{(R_1-R_2)}^2+h^2}+R_1^2+R_2^2]$

$=\frac{22}{7}[(6+2)\sqrt{{(6-2)}^2+8^2}+6^2+2^2]$

$=\frac{22}{7}[8\times 4\sqrt{5}+36+4]$

$=\frac{22}{7}[32\times 2.236+40]$

$=350.59{cm}^2$