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.
Cone will have a diameter and height of 14cm
∴ radius =7cm
Short height =√142+72
=√245=l
Surface area =πr2+πrl
=π(49)+π(7)√245=7π(7+√245)
Surface area of remaining solid = Total surface area of cube - Area of circle where cone carved out + curved surface area of cone.
=14×14×6−π×72+(π×7×7π(7+√245))=1366.344cm3