What is the area of a circle with a radius of 10?
Understand the Problem
The question is asking for the area of a circle given the radius. To find the area, we will use the formula A = πr², where r is the radius of the circle. Here, the radius is 10.
Answer
The area of the circle is \(314\).
Answer for screen readers
The area of the circle is (314).
Steps to Solve
- Identify the formula for the area of a circle
The formula to calculate the area (A) of a circle is given by:
$$ A = \pi r^2 $$
Where (r) is the radius.
- Substitute the radius into the formula
Given the radius (r = 10), we can substitute this value into the formula:
$$ A = \pi (10)^2 $$
- Calculate the area
Now we need to perform the calculation:
$$ A = \pi \cdot 100 $$
- Provide the numerical approximation for the area
Using the value of (\pi \approx 3.14), we find:
$$ A \approx 3.14 \cdot 100 = 314 $$
The area of the circle is (314).
More Information
The area of a circle is an important concept in geometry, often used in various applications such as architecture, engineering, and everyday calculations. The exact value of (\pi) can also lead to more precise results if calculated with more decimal places.
Tips
- Forgetting to square the radius. Always remember to raise (r) to the power of 2 before multiplying by (\pi).
- Using an incorrect value for (\pi). Ensure you use a sufficiently accurate value for (\pi) depending on the context.
