Question

A sphere is inscribed in a cylinder such that spere touches the cylinder . Show that the curved surface of spere is equal to the curved surface of cylinder.

Answer 1

A cylinder circumscribe a sphere is shown in figure Here , radius or sphere = radius of cylinder =r
Hight of cylinder h=2r
Now the curved surface of sphere=`4pi^(2)`
and the curved surface of cylinder = `2pirh=2pir(2r)=4pir^(2)`
Therefore the curved surface of sphere and curved surface of cylinder are equal.