If the surface area of a sphere increased by a factor of 3, by what factor did the radius of the sphere change?
A) 1.14
B) 1.73
C) 2.00
D) 2.24

Question

Quizplus · Accepted Answer

The surface area of a sphere is given by the formula S = 4πr^2, where r is the radius. If the surface area is increased by a factor of 3, then we have 3S = 4πr^2. Dividing both sides by 4π, we get 3S/4π = r^2. Taking the square root of both sides, we get r = sqrt(3S/4π). Hence, the radius of the sphere increases by a factor of sqrt(3) = 1.73. Therefore, the answer is (B).

If the Surface Area of a Sphere Increased by a Factor