If a circle has area 78.54 cm^2, what is its radius in centimeters?

If a circle has area 78.54 cm^2, what is its radius in centimeters?

• A. 7 cm
• B. 3 cm
• C. 5 cm
• D. 6 cm

Answer: (C)

The main idea is using the circle area formula A = πr^2 and solving for the radius. Solve for r: r = sqrt(A/π). With A = 78.54 cm^2, r^2 = 78.54 / π. Using π ≈ 3.1416 gives r^2 ≈ 25, so r ≈ 5 cm. Checking: π × 5^2 = π × 25 ≈ 78.54 cm^2, which matches the given area. Radii like 7, 3, or 6 would yield areas far from 78.54 cm^2, so 5 cm is consistent.

The main idea is using the circle area formula A = πr^2 and solving for the radius. Solve for r: r = sqrt(A/π). With A = 78.54 cm^2, r^2 = 78.54 / π. Using π ≈ 3.1416 gives r^2 ≈ 25, so r ≈ 5 cm. Checking: π × 5^2 = π × 25 ≈ 78.54 cm^2, which matches the given area. Radii like 7, 3, or 6 would yield areas far from 78.54 cm^2, so 5 cm is consistent.