Q6 of 51 Page 13

Prove that the surface area of a sphere is equal to curved surface area of the circumscribed cylinder.

Given: Radius of sphere = Radius of cylinder = r


To Prove: surface area of sphere = curved surface area of the circumscribed cylinder


Formula Used:


The curved surface area of cylinder = 2πrh


The surface area of sphere = 4πr2


Explanation:


For radius “r” units,


CSA of sphere = 4πr2


The height of cylinder = Diameter of sphere


= 2×Radius of sphere


= 2×r


= 2r units


Curved surface area of cylinder = 2πr(2r)


= 4πr2


Hence proved


More from this chapter

All 51 →
4

The surface area of a sphere is 616 cm2. Find its radius.

 5

A cylinder, a cone and a hemisphere of the equal base have the same height. What is their ratio in their volumes?

 7

Three cubes each of side 6 cm are joined end to end. Find the surface area and volume of the resulting cuboid.

 8

If the radii of the circular ends of a conical bucket which is 45 cm high are 28 cm and 7 cm, find the capacity of the bucket.

(Use π = 22/7)