Question

If a sphere's surface area is doubled, what is the corresponding change in radius?

a. the radius is increased to be 4 times the original size.
b. the radius is increased to be times the original size.
c. the radius is increased to be 2 times the original size.
d. the radius is increased to be 8 times the original size.

Answer 1

The radius is increased by sqrt2 times

It must be b

Answer 2

The radius is increased by \sqrt(2) times, so b must be the missing choice that we're looking for. The formula for sphere's surface area is 4*pi*r^2. When r is increased to be \sqrt(2)*r, the new surface area becomes 4*pi*(2*r^2)=8*pi*(r^2), doubling the original surface area.