Question

calculate and compare the surface area of sphere a, which has a radius of 5 in., and sphere b, which has a radius of 10 in. the formula for the surface area of a sphere is $4pi r^2$. (1 point) sphere a has a surface area of $20pi$ in.$^2$ and sphere b has a surface area of $40pi$ in.$^2$, meaning sphere bs surface area is 2 times as large as sphere as. sphere a has a surface area of $100pi$ in.$^2$ and sphere b has a surface area of $400pi$ in.$^2$, meaning sphere bs surface area is 4 times as large as sphere as. sphere a has a surface area of $5pi$ in.$^2$ and sphere b has a surface area of $10pi$ in.$^2$, meaning sphere bs surface area is 2 times as large as sphere as. sphere a has a surface area of $25pi$ in.$^2$ and sphere b has a surface area of $100pi$ in.$^2$, meaning sphere bs surface area is 4 times as large as sphere as.

Explanation:

Step1: Calculate surface area of Sphere A

The formula for the surface area of a sphere is \(4\pi r^2\). For Sphere A, \(r = 5\) in. Substitute \(r = 5\) into the formula:
\(4\pi(5)^2 = 4\pi\times25 = 100\pi\) in.²

Step2: Calculate surface area of Sphere B

For Sphere B, \(r = 10\) in. Substitute \(r = 10\) into the formula:
\(4\pi(10)^2 = 4\pi\times100 = 400\pi\) in.²

Step3: Compare the surface areas

To find how many times larger Sphere B's surface area is than Sphere A's, divide the surface area of Sphere B by that of Sphere A:
\(\frac{400\pi}{100\pi} = 4\)

Answer:

Sphere A has a surface area of \(100\pi\) in.² and sphere B has a surface area of \(400\pi\) in.², meaning sphere B's surface area is 4 times as large as sphere A's. (The corresponding option is the second one: Sphere A has a surface area of \(100\pi\) in.² and sphere B has a surface area of \(400\pi\) in.², meaning sphere B's surface area is 4 times as large as sphere A's.)