Question

how many times will the surface area of a sphere become if its radius is double

Answer 1

let the radius of the original sphere be r
then surface area of the sphere
= 4 x 22/7 x r x r
now the new radius of the sphere = 2r
surface area of new sphere
= 4 x 22/7 x 2r x 2r
now
area of original sphere/area of new sphere
=(4 x 22/7 x r x r)/(4 x 22/7 x 2r x 2r)
= 1/4
therefore
area of the new sphere
= 4(area of original sphere)

Answer 2

Surface area of a sphere whose radius is r is 4πr²
If the radius is doubled then substituting the value of r=2r in the formula we get
Surface area S=4π(2r)²
                        = 16πr²
So when we compare this to the original surface area of the sphere it is 4 times that of the original surface area

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