Question

act math practice exam
question 11/45
a formula for the surface area (a) of a sphere is $a = 4\pi r^2$ where r represents the radius. by doubling the dimension r, the surface area will be multiplied by what factor?
select one answer
a 2
b 4
c 8
d 10

Explanation:

Step1: Define original surface area

Let original radius be $r$. Original surface area: $A_1 = 4\pi r^2$

Step2: Calculate new surface area

Double radius to $2r$. New surface area: $A_2 = 4\pi (2r)^2 = 4\pi \cdot 4r^2 = 16\pi r^2$

Step3: Find scaling factor

Divide new by original area: $\frac{A_2}{A_1} = \frac{16\pi r^2}{4\pi r^2} = 4$

Answer:

B. 4