How does the surface area of a sphere change when the radius is tripled?A. The surface area doesn't changeB. The surface area is increased by 9C. The surface area is double…

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asked Feb 14, 2023 9.3k views

1 Answer

IMSoP · Answer 1 · 2023-02-19T06:38:39+0000

We must have in mind the surface of a sphere that is given by

$S_a=4\pi r^2$

When the radius of the sphere triples, the new radius becomes r1=3r. So, the new surface area of a sphere is

$S_(a1)=4\pi(3r)^2=9(4\pi r^2)=36\pi r^2$

As we can see, the surface area is multiplied by 9. The correct answer is D.