Area and Circumference of a Circle

The area of a circle is given by the formula: $$A = \frac{1}{2} \times \text{diameter} \times \text{radius}$$ or $$A = \text{π}r^2$$ , where r is the radius.

The circumference of a circle is given by the formula: $$C = 2\text{π}r$$ or $$C = \text{π}d$$ , where r is the radius and d is the diameter.

The area is $$A = \text{π}(7^2) = 49\text{π} \text{ cm}^2 \text{ (approximately 153.94 cm}^2)$$ .

Using the formula $$C = 2\text{π}r$$ , the radius is $$r = \frac{C}{2\text{π}} = \frac{31.4}{2\text{π}} \text{ (approximately 5 cm)}$$ .

The diameter is twice the radius: $$d = 2r$$ .

Using the formula $$C = \text{π}d$$ , the circumference is $$C = \text{π}(10) \text{ (approximately 31.4 inches)}$$ .

If the area is known, use the formula $$A = \text{π}r^2$$ and solve for r: $$r = \frac{\text{A}}{\text{π}}$$ .

The area is $$A = \text{π}(3^2) = 9\text{π} \text{ in}^2 \text{ (approximately 28.27 in}^2)$$ .

The circumference is $$C = 2\text{π}(4) = 8\text{π} \text{ cm} \text{ (approximately 25.13 cm)}$$ .

The diameter is $$d = 2r = 2(5) = 10 \text{ m}$$ .