If a circle has area 50π, what is the radius?

If a circle has area 50π, what is the radius?

• A. 5
• B. 10
• C. approximately 7.07
• D. 3.5

Answer: (C)

Area of a circle is π times the radius squared. If the area is 50π, set πr^2 = 50π. Divide both sides by π to get r^2 = 50, then r = sqrt(50) = 5√2 ≈ 7.07. The other radii would yield different areas: r = 5 gives 25π, r = 10 gives 100π, r = 3.5 gives 12.25π, none matching 50π.

Area of a circle is π times the radius squared. If the area is 50π, set πr^2 = 50π. Divide both sides by π to get r^2 = 50, then r = sqrt(50) = 5√2 ≈ 7.07.

The other radii would yield different areas: r = 5 gives 25π, r = 10 gives 100π, r = 3.5 gives 12.25π, none matching 50π.