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If the diameter of the sphere is doubled, the surface area of the resultant becomes $x$ times that of the original one. Then, what will be the value of $x$ ?

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answer is C.

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Detailed Solution

Given that the surface area of the sphere with doubled diameter becomes

x

times that of the original one.
We have the following formula,
Surface area = 4

π r 2

Radius will be,
=

2 d 2 = d

Surface area will be,

= 4 π (d) 2

= 4 π × 4 2 r 2

= 16 π r 2

= 4 × 4 π r 2

= 4

times the original one.

∴ x = 4

Thus the surface area of the resultant becomes 4 times that of the original one.
Therefore the correct option is 3.

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