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Question

If the height and diameter of a right circular cylinder are 32 cm and 6 cm respectively, then the radius of the sphere whose volume is equal to the volume of the cylinder is

A
3 cm
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B
4 cm
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C
6 cm
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D
None
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Solution

The correct option is C 6 cm

Volume of a Cylinder of Radius "R" and height "h" =πR2h

Radius of the cylinder =62=3cm
Hence, volume of the given cylinder =π×3×3×32cm3

Now, Volume of a sphere of radius 'r' =43πr3

$\Rightarrow \dfrac { 4 }{ 3 } \pi { r }^{ 3 } = \pi \times 3\times 3\times 32$
$\Rightarrow { r }^{ 3 } = 3 \times 3 \times 3 \times 8$
=>r=3×2=6cm


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