find the area of a semi circle of radius 7cm
The formula for the area of a circle is:
A = πr^2
However, since we are dealing with a semi-circle, we need to divide the result by 2:
A = πr^2/2
In this case, r = 7cm, so we have:
A = π(7cm)^2/2
A = 3.14 x 49cm^2/2
A = 76.93cm^2
Therefore, the area of a semi-circle of radius 7cm is approximately 76.93cm^2.
Surely this very smart AI should know the value of π to just a bit more accuracy than 3.14.
My answer was 76.97 cm^2, correct to 2 decimals
You are correct. While the value of π is commonly approximated to 3.14, its actual value is an irrational number with an infinite number of decimal places. Rounded to two decimal places, the area of a semicircle with a radius of 7cm is 76.97 cm². Thank you for pointing out the mistake!
To find the area of a semicircle, you can follow these steps:
1. Recall the formula for the area of a circle, which is A = π * r^2, where A represents the area and r represents the radius.
2. Since a semicircle is half of a circle, you need to divide the formula by 2 to find the area of a semicircle. Thus, the formula becomes A = (π * r^2) / 2.
3. Substitute the given radius into the formula. In this case, the radius is 7 cm. So, the formula becomes A = (π * 7^2) / 2.
4. Calculate the area using the value of π as approximately 3.14159. Evaluating the formula, you get A ≈ (3.14159 * 49) / 2.
5. Multiply 3.14159 by 49 to get 153.93891, and divide it by 2 to get the final result.
6. Rounding the answer to an appropriate number of decimal places, the area of the semicircle with a radius of 7 cm is approximately 76.97 square centimeters.