Q:

Determine the area of the shaded region. Use 3 for pi. A.196 square inches B.294 square inches C.462 square inches D.588 square inchesFirst to answer gets brainlyest please hurry

Accepted Solution

A:
Answer:The correct option is B) 294 square inches Step-by-step explanation:Consider the provided informationThere are two circles inscribed in a circle.The two circles touch each other at one point and each one touch the bigger circle at one point.The radius of the smaller circle is 7 inches.The diameter of the bigger circle = sum of the diameters of the two smaller circle.The diameter of smaller circle is = 2 × 7 = 14 inchesTherefore, the diameter of the bigger circle = 14 + 14 = 28 inchesThe radius bigger circle is 28/2 = 14 inchesArea of the shaded part =  Area of bigger circle - Area of both smaller circle.Area of bigger circle = πr²Area of bigger circle = 3 × 14² (π=3 given)Area of bigger circle = 588 inches²Area of smaller circle = 3 × 7² (π=3 given)Area of smaller circle = 147 inches²We have two smaller circle, so the area of of two smaller circles = 2 × 147 = 294 inches²Area of the shaded part = Area of bigger circle - Area of both smaller circle.Area of the shaded part =  588 - 294 = 294 inches²Hence, the area of the shaded region is 294 square inches.Therefore, the correct option is B) 294 square inches