Question

A right circular cylinder just encloses a sphere of radius r (see Fig. 13.22). Find:
(i) surface area of the sphere,
(ii) curved surface area of the cylinder,
(iii) ratio of the areas obtained in

Answer 1

According to the problem given ,

Radius of the Sphere = r

Radius of the Right circular cylinder

= r

Height of the cylinder ( h ) = 2r

i )Surface area of Sphere (A1) = 4πr² ---( 1 )

ii ) Curved surface area

of the Cylinder ( A2) = 2πrh

= 2πr × 2r

= 4πr² -----( 2 )

iii )Ratio of the areas = ( A1) : (A2)

= ( 4πr² ) : ( 4πr² )

= 1 : 1

I hope this helps you.

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Answer 2

Given, radius of the cylinder = r.

Height of the cylinder = h = 2r.

(i)

Surface area of the sphere = 4πr².

(ii)

Curved Surface area of the cylinder = 2πrh

                                                            = 2πr(2r)

                                                            = 4πr².

(iii)

Ratio of the area:

⇒ Surface area/Curved surface area

⇒ 4πr²/4πr²

⇒ 1:1.

Hope it helps!