if the radius of a sphere is doubled the surface

Question

If the radius of a sphere is doubled, the surface area is

a. multiplied by 4.

b. multiplied by 2.

c. multiplied by 3.

d. multiplied by 8.

a. The formula for the surface area of a sphere is 4πr². If the radius is doubled, this implies that the radius is also doubled. The formula then becomes 4π(2r)². Solve this expression, 4π(4r²) equals 16πr². Compare 4πr² to 16πr²; 16πr² is 4 times greater than 4πr². Thus, the surface area is four times as great.