Question

Find the surface area of the biggest sphere which can fit inside a cube of side 4a.

Answer 1

From given information we can say that " The biggest sphere that can fit inside a cube of side 4 a will have a diameter of 4a (anything larger will not fit in, as opposite sides are separated by a distance of 4a.) "

So,

Diameter of sphere = 4 a , So Radius of sphere =2a

We know surface area of sphere = 4 π r2 , So

Surface area of sphere = 4 π (2 a )2 = 4 π (4a2 ) = 16π a2