Question

calculate and compare the surface area of sphere a, which has a radius of 2 in, and sphere b, which has a radius of 10 in. the formula for the surface area of a sphere is 4πr².
sphere a has a surface area of 8π in.² and sphere b has a surface area of 40π in.², meaning sphere b’s surface area is 5 times as large as sphere a’s.
sphere a has a surface area of 16π in.² and sphere b has a surface area of 400π in.², meaning sphere b’s surface area is 25 times as large as sphere a’s.
sphere a has a surface area of 2π in.² and sphere b has a surface area of 10π in.², meaning sphere b’s surface area is 4 times as large as sphere a’s.
sphere a has a surface area of 4π in.² and sphere b has a surface area of 100π in.², meaning sphere b’s surface area is 25 times as large as sphere a’s.

Explanation:

Step1: Calculate surface area of Sphere A

The formula for the surface area of a sphere is \( SA = 4\pi r^{2} \). For Sphere A, radius \( r_A = 2 \) in. Substitute \( r = 2 \) into the formula:
\( SA_A = 4\pi(2)^{2} = 4\pi\times4 = 16\pi \) square inches.

Step2: Calculate surface area of Sphere B

For Sphere B, radius \( r_B = 10 \) in. Substitute \( r = 10 \) into the surface area formula:
\( SA_B = 4\pi(10)^{2} = 4\pi\times100 = 400\pi \) square inches.

Step3: Find the ratio of \( SA_B \) to \( SA_A \)

To find how many times larger \( SA_B \) is than \( SA_A \), divide \( SA_B \) by \( SA_A \):
\( \frac{SA_B}{SA_A} = \frac{400\pi}{16\pi} \). The \( \pi \) terms cancel out, so \( \frac{400}{16} = 25 \).

Answer:

Sphere B's surface area is 25 times as large as Sphere A's (matching Item 14's description: "Sphere A has a surface area of \( 16\pi \) in.² and Sphere B has a surface area of \( 400\pi \) in.², meaning sphere B’s surface area is 25 times as large as sphere A’s").