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A right circular cylinder just encloses...

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  (i) and (ii).

Text Solution

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Diameter of sphere=diameter of cylinder
Radius of sphere=radius of cylinder
Height of cylinder=Diameter of sphere
Height of cylinder=2r of sphere
a) Surface area of sphere=`4pir^2`
b) Curved surface area of Cylinder=`2pirH=2pir(2r)=2pir^2`
c) ratio=`(4pir^2)/(4pir^2)=1`.
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Knowledge Check

  • The ratio of the surface area of a sphere and the curved surface area of the cylinder circumscribing the sphere is

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    `1:2`
    B
    `1:1`
    C
    `2:1`
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    C
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    D
    `3:1`

  • A sphere and a cylinder have equal volume and equal radius. The ratio of the curved surface area of the cylinder to that of the sphere is

    A
    `4:3`
    B
    `2:3`
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    D
    `3:4`

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