Answer:
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
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