What is the formula to calculate the area of a circle given its radius?

What is the formula to calculate the area of a circle given its radius?

• A. A = π r^2
• B. C = π d
• C. V = 4/3 π r^3
• D. A = 2 π r

Answer: (A)

Area grows with the radius, and for a circle that growth is proportional to the radius squared. So the way to find the amount of space inside a circle when you know its radius is A = π r^2. This captures how the area increases as the circle gets bigger, since you’re effectively layering many tiny slices whose total area scales with the square of the radius. As a quick check, if the radius is 5 units, the area is 25π square units, about 78.5. Other formulas describe different things. A = 2πr is the circumference, the distance around the circle. C = π d would give circumference if you’re using the diameter. V = 4/3 π r^3 is the volume of a sphere, not a circle.

Area grows with the radius, and for a circle that growth is proportional to the radius squared. So the way to find the amount of space inside a circle when you know its radius is A = π r^2. This captures how the area increases as the circle gets bigger, since you’re effectively layering many tiny slices whose total area scales with the square of the radius. As a quick check, if the radius is 5 units, the area is 25π square units, about 78.5.

Other formulas describe different things. A = 2πr is the circumference, the distance around the circle. C = π d would give circumference if you’re using the diameter. V = 4/3 π r^3 is the volume of a sphere, not a circle.