The radius of a circle is 5 in. Find its area to the nearest whole number.
Understand the Problem
The question is asking to calculate the area of a circle with a radius of 5 inches, and then round the result to the nearest whole number. The formula for the area of a circle is A = πr², where r is the radius.
Answer
$79$ in²
Answer for screen readers
The area of the circle is approximately $79$ in².
Steps to Solve
- Identify the radius
The radius of the circle is given as $r = 5$ inches.
- Apply the formula for area
Use the area formula for a circle:
$$ A = \pi r^2 $$
Substituting the value of the radius:
$$ A = \pi (5)^2 $$
- Calculate the area
Calculate $5^2$ first:
$$ 5^2 = 25 $$
Now substituting back into the area formula:
$$ A = \pi \times 25 $$
- Approximate the value of π
Using the approximation $\pi \approx 3.14$,
$$ A \approx 3.14 \times 25 $$
- Perform the multiplication
Calculating $3.14 \times 25$:
$$ A \approx 78.5 $$
- Round to the nearest whole number
Now, round $78.5$ to the nearest whole number, which gives $79$.
The area of the circle is approximately $79$ in².
More Information
The area of a circle grows rapidly with its radius. For example, if the radius were to double, the area would increase fourfold, due to the $r^2$ factor in the area formula.
Tips
- A common mistake is forgetting to square the radius before multiplying by π.
- Another mistake is rounding too early in the calculations instead of at the final result.
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