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 from the figure :

Diameter of sphere = Diameter of Cyl.

Radius of Cyl. = Radius of sphere

Height of Cyl. = Diameter of sphere

Surface area of sphere = 4 π r²

Lateral surface area of Cyl. = 2 π r h × 2r

= 4 π r²

Hence its prove that :

Surface area of sphere = Lateral surface area of Cyl.

Thank you