Question

A cone of maximum size is carved out from a cube of edge $14cm$. Find the surface area of the remaining solid after the cone is carved out.

Answer 1

Cone will have a diameter and height of $14cm$

$\therefore$ radius $=7cm$

Short height $=\sqrt{{14}^2+7^2}$

$=\sqrt{245}=l$

Surface area $=\pi r^2+\pi rl$

$=\pi \left(49\right)+\pi \left(7\right)\sqrt{245}=7\pi (7+\sqrt{245})$

Surface area of remaining solid $=$ Total surface area of cube - Area of circle where cone carved out + curved surface area of cone.

$=14\times 14\times 6-\pi \times 7^2+(\pi \times 7\times 7\pi (7+\sqrt{245}))=1366.344c{m}^3$