Determine the area of the shaded region. use 3 for pi.
196 square inches
294 square inches
462 square inches
588 square inches
ty!

The area of the shaded region is 294 square inches ⇒ 2nd answer

Step-by-step explanation:

* Lets explain how to solve the problem

- From the attached figure

- There are two congruent circles inscribed in a circle

∵ The two congruent circles touch each other at one point and

   each one touch the big circle at one point

∴ The centers of the three circles and the touches' points lie on

   the same segment which is the diameter of the big circle

∴ The diameter of the big circle = the sum of the diameters of the

   inscribed circles

∵ The radii of the congruent circle = 7 inches

∵ The diameter of a circle is twice its radius

∴ The diameter of each inscribed circle = 2 × 7 = 14 inches

∴ The diameter of the big circle = 14 + 14 = 28 inches

∵ The radius of a circle is half its diameter

∴ The radius of the big circle = 1/2 × 28 = 14 inches

- The area of the shaded part is the difference between the area

  of the big circle and the sum of areas of the congruent circles

∵ The area of a circle = πr²

∵ The radius of the big circle is 14 inches

∵ π = 3 ⇒ given

∴ The area of the big circle = 3(14)² = 588 inches²

∵ The radius of each congruent circle is 7 inches

∴ The area of each congruent circles = 3(7)² = 147 inches²

∴ The area of the two congruent circles = 2 × 147 = 294 inches²

∵ Area shaded = area big circle - area two congruent circles

∴ Area shaded = 588 - 294 = 294 inches²

* The area of the shaded region is 294 square inches

the answer is 13 cm