Question

Show if the total surface area of a sphere is same that of the total lateral surface of a right circular cylinder and if that is enclosed.

Answer 1

$\mathfrak{\large {\underline {\underline{Answer \: : - }}}}$

Proved !!

$\mathfrak { \large{\underline {\underline{Explanation \: : - }}}}$

Let the radius of the sphere be r cm.

Then,

Surface area of the sphere = 4πr² cm²　　　　　 　　　　　　 ...(i)

The radius and height of a right circular cylinder that just encloses the sphere of radius r and 2r respectively.

Surface area of the cylinder = 2πr x 2r

= 4πr² cm²　　　　　　　　...(ii)

From (i) and (ii), we have

Surface area of the sphere is equal to the surface area of the cylinder that just encloses the sphere.

Answer 2

Explanation:

Let the radius of sphere be ' r '

So from the figure :

Diameter of Cyl. = Diameter of sphere ....

Radius of Cyl. = Radius of sphere.....

Height of Cyl. = Diameter of sphere ....

Surface area of sphere ( S.A ) = 4πr²

Lateral surface area of Cyl. = 2πrh × 2r

= 4πr²

Hence it proved

Surface area of sphere = Lateral surface area of Cyl.

Thank you