Answer :
Let's find the diameter of a circle given that the area is 615.75 square inches. We will be using the formula for the area of a circle and solving for the radius and subsequently the diameter.
### Step-by-Step Solution:
1. Understand the formula for the area of a circle:
[tex]\[ A = \pi r^2 \][/tex]
where [tex]\(A\)[/tex] is the area of the circle, [tex]\(r\)[/tex] is the radius of the circle, and [tex]\(\pi\)[/tex] (pi) is approximately 3.14159.
2. Given:
[tex]\[ A = 615.75 \text{ square inches} \][/tex]
3. Rearrange the formula to solve for the radius [tex]\(r\)[/tex]:
[tex]\[ r = \sqrt{\frac{A}{\pi}} \][/tex]
4. Substitute the given area into the formula:
[tex]\[ r = \sqrt{\frac{615.75}{\pi}} \][/tex]
5. Calculate the radius [tex]\(r\)[/tex] (using the provided accurate result):
[tex]\[ r \approx 13.999975443466646 \text{ inches} \][/tex]
6. Now, the diameter [tex]\(d\)[/tex] of a circle is twice the radius:
[tex]\[ d = 2r \][/tex]
7. Substitute the radius into the formula for the diameter:
[tex]\[ d = 2 \times 13.999975443466646 \][/tex]
8. Calculate the diameter [tex]\(d\)[/tex]:
[tex]\[ d \approx 27.99995088693329 \text{ inches} \][/tex]
Hence, the diameter of the circle with an area of 615.75 square inches is approximately 27.99995088693329 inches.
### Step-by-Step Solution:
1. Understand the formula for the area of a circle:
[tex]\[ A = \pi r^2 \][/tex]
where [tex]\(A\)[/tex] is the area of the circle, [tex]\(r\)[/tex] is the radius of the circle, and [tex]\(\pi\)[/tex] (pi) is approximately 3.14159.
2. Given:
[tex]\[ A = 615.75 \text{ square inches} \][/tex]
3. Rearrange the formula to solve for the radius [tex]\(r\)[/tex]:
[tex]\[ r = \sqrt{\frac{A}{\pi}} \][/tex]
4. Substitute the given area into the formula:
[tex]\[ r = \sqrt{\frac{615.75}{\pi}} \][/tex]
5. Calculate the radius [tex]\(r\)[/tex] (using the provided accurate result):
[tex]\[ r \approx 13.999975443466646 \text{ inches} \][/tex]
6. Now, the diameter [tex]\(d\)[/tex] of a circle is twice the radius:
[tex]\[ d = 2r \][/tex]
7. Substitute the radius into the formula for the diameter:
[tex]\[ d = 2 \times 13.999975443466646 \][/tex]
8. Calculate the diameter [tex]\(d\)[/tex]:
[tex]\[ d \approx 27.99995088693329 \text{ inches} \][/tex]
Hence, the diameter of the circle with an area of 615.75 square inches is approximately 27.99995088693329 inches.
