What is the area of a circle with a radius of 11 inches?
Understand the Problem
The question is asking for the area of a circle with a radius of 11 inches. To find the area, we will use the formula A = πr², where r is the radius of the circle.
Answer
The area of the circle is approximately $A \approx 380.14$ square inches.
Answer for screen readers
The area of the circle is approximately $A \approx 380.14$ square inches.
Steps to Solve
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Identify the formula for the area of a circle To find the area, we use the formula $A = \pi r^2$, where $A$ is the area and $r$ is the radius.
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Substitute the radius into the formula We have a radius of 11 inches, so we substitute $r = 11$ into the formula: $$ A = \pi (11)^2 $$
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Calculate the square of the radius Now we calculate $11^2$: $$ 11^2 = 121 $$
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Multiply by π Next, we multiply the result by $\pi$: $$ A = \pi \times 121 $$
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Express the final result This gives us the final area: $$ A \approx 3.14 \times 121 \approx 380.14 $$ (using $\pi \approx 3.14$)
The area of the circle is approximately $A \approx 380.14$ square inches.
More Information
The area of a circle is a fundamental concept in geometry. Using the radius to calculate the area provides a clear understanding of how the size of a circle expands with its radius.
Tips
- Forgetting to square the radius before multiplying by π. Always compute $r^2$ first.
- Confusing the diameter with the radius. Remember, the radius is half the diameter.
