Question

what is the change in volume and surface area of a sphere if its radius become three times

Answer 1

The surface area A of a sphere of radius ris given by

A=4πr2A=4πr2

So let’s suppose that the radius r was reduced to half its size. The new radius rnrnwould be given by

rn=r/2rn=r/2

The surface area AnAn of the new sphere would be

AnAn =4πr2n=4π(r/2)2=(4πr2)(1/4)=14A=4πrn2=4π(r/2)2=(4πr2)(1/4)=14A

Therefore, if the radius of a sphere is reduced to half its size, the sphere’s surface area is reduce to 1/4 its initial value.



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