Area and Circumference of Circles

The area A of a circle is given by the formula: $$A = \pi r^2$$ , where r is the radius.

The circumference C of a circle is given by the formula: $$C = 2 \pi r$$ or $$C = \pi d$$ , where d is the diameter.

The diameter is the distance across the circle through its center, equal to twice the radius: $$d = 2r$$ .

The diameter is $$d = 2r = 2 \times 5 = 10 cm$$ .

Using the formula $$A = \pi r^2$$ , the area is $$A = \pi \times 3^2 = 28.27 cm^2$$ (approximately).

Using the formula $$C = 2 \pi r$$ , the circumference is $$C = 2 \times \pi \times 4 = 25.13 cm$$ (approximately).

The radius is half the diameter: $$r = \frac{d}{2} = \frac{12}{2} = 6 cm$$ .

First, find the radius: $$r = \frac{10}{2} = 5 inches$$ . Then, $$A = \pi r^2 = \pi \times 5^2 = 78.54 in^2$$ (approximately).

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

Using the area formula, $$A = \pi r^2$$ , we can solve for r: $$r = \sqrt{\frac{A}{\pi}} = \sqrt{\frac{50.24}{\pi}} = 4 in$$ (approximately).