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

$\mathfrak {\underline {\underline{Answer }}}$

Proved !!

$\mathfrak {\underline {\underline{Explanation }}}$

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 As from figure :

Diameter of Cylinder = Diameter of sphere .

Radius of sphere = Radius of Cylinder .

Height of Cylinder = Diameter of sphere .

Surface area of sphere = 4πr²

Lateral surface Area of Cylinder = 2πrh × 2r

= 4πr²

Hence proved .....

Surface area of sphere = Lateral surface area of Cylinder....

Thank you