To find the area of a quarter circle with a diameter of 10 inches, follow these steps:
1. Determine the radius:
- The radius is half of the diameter.
- Given the diameter is 10 inches:
[tex]\[
\text{radius} = \frac{\text{diameter}}{2} = \frac{10 \text{ inches}}{2} = 5 \text{ inches}
\][/tex]
2. Calculate the area of the full circle:
- The formula for the area of a circle is:
[tex]\[
\text{Area} = \pi \times \text{radius}^2
\][/tex]
- Here, the radius is 5 inches, and [tex]\(\pi\)[/tex] is approximately 3.14:
[tex]\[
\text{Area} = 3.14 \times (5 \text{ inches})^2 = 3.14 \times 25 = 78.5 \text{ square inches}
\][/tex]
3. Determine the area of the quarter circle:
- A quarter circle is one-fourth of a full circle.
[tex]\[
\text{quarter circle area} = \frac{\text{full circle area}}{4} = \frac{78.5 \text{ square inches}}{4} = 19.625 \text{ square inches}
\][/tex]
4. Round the answer to the nearest hundredth:
- The area of the quarter circle is 19.625 square inches. When rounded to the nearest hundredth:
[tex]\[
\text{Rounded area} = 19.62 \text{ square inches}
\][/tex]
Therefore, the area of the quarter circle is [tex]\(19.62 \, \text{in}^2\)[/tex].
