Circle: radius, diameter, circumference and area

A circle is a shape consisting of all points are the same distance from the center.

The radius is the distance between any point of the circle and the centre. The diameter is a line segment which goes straight across the circle and passes through the centre. The diameter is twice the radius: $D=2R$. The circumference is the distance around the circle. It can be calculated by these formulas below:

$$C=\pi D=2\pi R$$

The area enclosed by a circle can be calculated by this formula below:

$$A=\pi R^2$$

Solved examples

What is the circumference of a circle with radius of 3.5 cm? Round your answer to the nearest one.

$$C=2\pi R=2\cdot 3.14\cdot 3.5 \approx 22 \text{ cm}$$

What is the area of a circle with diameter of 5 cm? Round your answer to the nearest one.

$$A=\pi R^2=3.14\cdot \left (\frac{5}{2} \right )^2 \approx 20 \text{ cm}^2$$

What is the area of a circle with circumference of 30 cm? Round your answer to the nearest one.

$$C=2\pi R, \ \ 30=2\pi R, \ \ R=\frac{15}{\pi}$$ $$A=\pi R^2=3.14\cdot \left (\frac{15}{3.14} \right )^2 \approx 72 \text{ cm}^2$$

2021-08-24