The diameter of a circle is 8 inches. Find the area in terms of pi.
The Correct Answer and Explanation is:
To find the area of a circle when the diameter is given, we use the formula for the area of a circle:A=πr2A = \pi r^2A=πr2
Where:
- AAA is the area,
- rrr is the radius of the circle,
- π\piπ is approximately 3.14159, but we will leave it as π\piπ for the exact form.
Step 1: Find the radius
The radius rrr is half of the diameter. Since the diameter is 8 inches, we divide it by 2 to get the radius:r=82=4 inchesr = \frac{8}{2} = 4 \, \text{inches}r=28=4inches
Step 2: Apply the radius to the area formula
Now that we know the radius is 4 inches, we substitute this value into the area formula:A=πr2=π(4)2=π×16A = \pi r^2 = \pi (4)^2 = \pi \times 16A=πr2=π(4)2=π×16
Step 3: Simplify the expression
The area is:A=16π square inchesA = 16\pi \, \text{square inches}A=16πsquare inches
Conclusion:
The area of the circle, in terms of π\piπ, is 16π16\pi16π square inches. This result expresses the exact area of the circle without approximating π\piπ. If you wanted to find an approximate value, you could substitute π≈3.14159\pi \approx 3.14159π≈3.14159, but in this case, the exact expression 16π16\pi16π is preferred.
This method demonstrates how the relationship between diameter and radius is crucial when solving for properties like area. By remembering that the radius is half the diameter, you can easily substitute into the formula to find the area of any circle.
