Question

Circle Y has a central angle Angle XYZ , which forms the shaded segment shown. If the area of the segment is approximately 4.64 square inches and m angle XYZ = 90 degrees °, what is the radius of circle ? round your answer to the nearest integer inches

Answer 1

The radius of the circle is approximately 3.54 inches.

Step-by-step explanation:

To find the radius of the circle, we need to first find the area of the whole circle using the formula A = πr². Given that the area of the shaded segment is approximately 4.64 square inches and the central angle XYZ is 90 degrees, we know that the shaded segment is one-fourth of the total area of the circle. So, we can set up the equation:

4.64 = (πr²)/4

12.5 = r²

r ≈ √12.5 ≈ 3.54 inches

Therefore, the radius of the circle is approximately 3.54 inches when rounded to the nearest integer.