Answer :
To determine the area of a circle with a diameter of 16.2 inches, follow these steps:
1. Calculate the radius of the circle:
The radius is half the diameter. Given that the diameter is 16.2 inches:
[tex]\[ \text{radius} = \frac{\text{diameter}}{2} = \frac{16.2}{2} = 8.1 \text{ inches} \][/tex]
2. Use the formula for the area of a circle:
The formula for the area [tex]\(A\)[/tex] of a circle is:
[tex]\[ A = \pi r^2 \][/tex]
where [tex]\(\pi\)[/tex] is approximately 3.14, and [tex]\(r\)[/tex] is the radius calculated in step 1.
3. Substitute the radius and [tex]\(\pi\)[/tex] into the formula:
[tex]\[ A = 3.14 \times (8.1)^2 \][/tex]
4. Calculate the area:
[tex]\[ (8.1)^2 = 65.61 \][/tex]
[tex]\[ A = 3.14 \times 65.61 = 206.0154 \text{ square inches} \][/tex]
5. Round the area to the nearest hundredth:
The value 206.0154 rounded to the nearest hundredth is 206.02.
Thus, the area of the circle is:
[tex]\[ \boxed{206.02 \text{ in}^2} \][/tex]
1. Calculate the radius of the circle:
The radius is half the diameter. Given that the diameter is 16.2 inches:
[tex]\[ \text{radius} = \frac{\text{diameter}}{2} = \frac{16.2}{2} = 8.1 \text{ inches} \][/tex]
2. Use the formula for the area of a circle:
The formula for the area [tex]\(A\)[/tex] of a circle is:
[tex]\[ A = \pi r^2 \][/tex]
where [tex]\(\pi\)[/tex] is approximately 3.14, and [tex]\(r\)[/tex] is the radius calculated in step 1.
3. Substitute the radius and [tex]\(\pi\)[/tex] into the formula:
[tex]\[ A = 3.14 \times (8.1)^2 \][/tex]
4. Calculate the area:
[tex]\[ (8.1)^2 = 65.61 \][/tex]
[tex]\[ A = 3.14 \times 65.61 = 206.0154 \text{ square inches} \][/tex]
5. Round the area to the nearest hundredth:
The value 206.0154 rounded to the nearest hundredth is 206.02.
Thus, the area of the circle is:
[tex]\[ \boxed{206.02 \text{ in}^2} \][/tex]
