Mensuration (C10)

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

Answer

Surface area of remaining solid = 6L2 - πr2 + πrℓ, where r and l are the radius and slant height of the cone.

ℓ = √(72 + 142) = 7√5

L = 14 cm

r = 14/2 = 7 cm

Surface area of remaining solid = (1022 + 154√5) cm2