Find the area of each. Use [3.14] for the value of [pi]. Round your answer to the nearest hundredth if r = 8.6 in.
Understand the Problem
The question is asking for the area of a circle given the radius. To solve it, we will use the formula A = π × r², substituting the radius (r = 8.6 in) and using π ≈ 3.14. We then round the answer to the nearest hundredth.
Answer
The area of the circle is approximately $232.30 \, \text{in}^2$.
Answer for screen readers
The area of the circle is approximately $232.30 , \text{in}^2$.
Steps to Solve
- Identify the formula for the area of a circle
The formula to calculate the area of a circle is given by:
$$ A = \pi \times r^2 $$
- Substitute the given values into the formula
Here, the radius ( r = 8.6 ) inches. Using ( \pi \approx 3.14 ):
$$ A = 3.14 \times (8.6)^2 $$
- Calculate the square of the radius
First, calculate ( (8.6)^2 ):
$$ (8.6)^2 = 73.96 $$
- Multiply by π
Now substitute this value back into the area formula:
$$ A = 3.14 \times 73.96 $$
- Perform the multiplication
Calculating gives:
$$ A \approx 232.2984 $$
- Round to the nearest hundredth
After rounding:
$$ A \approx 232.30 $$
The area of the circle is approximately $232.30 , \text{in}^2$.
More Information
The area of a circle is dependent on the square of its radius and is scaled by the value of π. Using a value of ( \pi ) such as 3.14 is common for simple calculations.
Tips
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Forgetting to square the radius before multiplying it by π. Always calculate ( r^2 ) first.
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Misplacing decimals when doing multiplication, especially with decimal numbers.
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