Ask Question
18 April, 02:21

Express answer in exact form.

Find the area of one segment formed by a square with sides of 6" inscribed in a circle.

(Hint: use the ratio of 1:1:√2 to find the radius of the circle.)

+1
Answers (1)
  1. 18 April, 02:28
    0
    The answer is 5.13 in²

    Step 1. Calculate the diameter of the circle (d).

    Step 2. Calculate the radius of the circle (r).

    Step 3. Calculate the area of the circle (A1).

    Step 4. Calculate the area of the square (A2).

    Step 5. Calculate the difference between two areas (A1 - A2) and divide it by 4 (because there are total 4 segments) to get the area of one segment formed by a square with sides of 6" inscribed in a circle.

    Step 1:

    The diameter (d) of the circle is actually the diagonal (D) of the square inscribed in the circle. The diagonal (D) of the square with side a is:

    D = a√2 (ratio of 1:1:√2 means side a : side a : diagonal D = 1 : 1 : √2)

    If a = 6 in, then D = 6√2 in.

    d = D = 6√2 in

    Step 2.

    The radius (r) of the circle is half of its diameter (d):

    r = d/2 = 6√2 / 2 = 3√2 in

    Step 3.

    The area of the circle (A1) is:

    A = π * r²

    A = 3.14 * (3√2) ² = 3.14 * 3² * (√2) ² = 3.14 * 9 * 2 = 56.52 in²

    Step 4.

    The area of the square (A2) is:

    A2 = a²

    A2 = 6² = 36 in²

    Step 5:

    (A1 - A2) / 4 = (56.52 - 36) / 4 = 20.52/4 = 5.13 in²
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Express answer in exact form. Find the area of one segment formed by a square with sides of 6" inscribed in a circle. (Hint: use the ratio ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers