Question

A sphere fits exactly into a cylinder, i.e. the sphere touches the cylinder at the top, the bottom and the curved
surface. Show that the surface area of the sphere is equal to the area of the curved surface of the cylinder.
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Answer 1

Answer:

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.

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Text Solution

Solution

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=4π2

and the curved surface of cylinder = 2πrh=2πr(2r)=4πr2

Therefore the curved surface of sphere and curved surface of cylinder are equal.