(Answer correct to 1 decimal place.) The surface area of a sphere is given by the formula $A=4 \pi r^{2}$, where $r$ is the radius of the sphere. a. Find the surface area of a sphere that has a radius of $5 \mathrm{~cm}$. b. What is the radius of a sphere that has a surface area equal to $500 \mathrm{~cm}^{2}$ ? (Answer correct to the nearest mm.)

Step 1 ：a. Calculate the surface area of a sphere with a radius of 5 cm: \(A = 4 \pi (5)^{2} \approx 314.2 \, cm^{2}\)

Step 2 ：b. Find the radius of a sphere with a surface area of 500 cm²: \(r = \sqrt{\frac{500}{4 \pi}} \approx 6.3 \, cm \) (or \(63 \, mm\), rounded to the nearest mm)

Step 3 ：\boxed{\text{Final Answer:}}

Step 4 ：a. \boxed{314.2 \, cm^{2}}

Step 5 ：b. \boxed{6.3 \, cm \, (63 \, mm)}