How can I work out the area of a semi-circle with a diameter of 12cm?
To work out the area of a semi-circle with a diameter of 12cm, you can follow these steps:
- Find the radius of the semi-circle by dividing the diameter by 2: radius = diameter / 2 = 12cm / 2 = 6cm
- Calculate the area of the full circle with the same radius using the formula: area = π * radius^2 where π (pi) is a mathematical constant equal to approximately 3.14159.In this case, the radius is 6cm, so the area of the full circle is: area = π * 6^2 = 113.1cm^2
- Divide the area of the full circle by 2 to get the area of the semi-circle: area of semi-circle = area of full circle / 2 = 113.1cm^2 / 2 = 56.55cm^2
Therefore, the area of the semi-circle with a diameter of 12cm is approximately 56.55cm^2.
The formula for finding the area of a semi-circle is (πr^2)/2, where r is the radius of the semi-circle. In this case, the diameter is 12cm, so the radius would be 6cm. Plugging this value into the formula, we get (π6^2)/2, which simplifies to 28.27cm^2.
A semi-circle is a half-circle, while a circle is a two-dimensional shape with no angles or corners, and a constant radius. The formula for finding the area of a circle is πr^2, while the formula for finding the area of a semi-circle is (πr^2)/2.
Calculating the area of a semi-circle can be useful in a variety of fields, such as architecture, engineering, and construction. For example, knowing the area of a semi-circular arch can help architects design buildings with appropriate structural support, while engineers can use this information to calculate the stress and strain on a semi-circular bridge support.
The diameter of a semi-circle is important because it is used to determine the radius, which is a key component in the formula for finding the area of a semi-circle. By dividing the diameter by 2, you can find the radius, which is then squared and multiplied by π to find the area.
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