Question

a right circular cylinder just encloses a sphere of radius r

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Find :- curved surface area of that cylinder
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Find :- ratio of areas of cylinder and sphere
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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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Answer 2

Given:-

• Radius of sphere = r
• Radius of sphere = Radius of cylinder = r
• Height of cylinder = 2r

Solution:-

1) Curved Surface Area=2πrh

⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀=2πr(2r)=4πr²

2) Ratio = $\frac{4\pir^2}{4\pir^2}$

= $\frac{1}{1}$

or 1:1