To find the area of a circle, you use the formula:
Area=π×r2\text{Area}=\pi \times r^2Area=π×r2
where rrr is the radius of the circle, and π\pi π (pi) is approximately 3.14 or 227\frac{22}{7}722
Steps to find the area:
- Determine the radius rrr of the circle. If you only have the diameter ddd, you can find the radius by halving the diameter:
r=d2r=\frac{d}{2}r=2d
- Substitute the radius into the formula and square it.
- Multiply by π\pi π.
Alternatively, if you know the diameter ddd, you can use:
Area=π×(d2)2=πd24\text{Area}=\pi \times \left(\frac{d}{2}\right)^2=\frac{\pi d^2}{4}Area=π×(2d)2=4πd2
If you know the circumference CCC, you can also find the area using:
Area=C24π\text{Area}=\frac{C^2}{4\pi}Area=4πC2
Example:
If a circle has a diameter of 40 cm:
- Radius r=402=20r=\frac{40}{2}=20r=240=20 cm
- Area =π×202=3.14×400=1256=\pi \times 20^2=3.14\times 400=1256=π×202=3.14×400=1256 cm² (approximately)
- Rounded to three significant figures, the area is 1260 cm²
This formula gives the amount of space inside the circle, measured in square units (e.g., cm², m²)
. In summary, the key formula to remember is:
Area=πr2\boxed{\text{Area}=\pi r^2}Area=πr2
where rrr is the radius of the circle
