Question

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1) A right circular cylinder just encloses a sphere of radius r as shown in fig 6.12. The surface area of sphere is equal to the curved surface area of a cylinder.

Answer 1

Given:

Radius of
sphere=r

Radius of
cylinder= Radius of sphere=r

Height of cylinder=
diameter= 2r

 

(i)   The surface area
of the sphere with radius r (A1)= 4πr²

(ii)

 Curved surface of cylinder (A2)=2πrh



= 2π × r × 2r

= 4πr²



(iii) Required ratio of the areas = A1:A2

= 4πr²:4πr² =
1:1

Ratio of the areas obtained= 1:1

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