Multiple choice

The sum of circumference of a circle and perimeter of a rectangle is 132 cm. The area of the rectangle is 112 sq. cm and its breadth is 8 cm. What is the area of the circle?

  1. 616 sq. cm

  2. 540 sq. cm

  3. 396 sq. cm

  4. 390 sq. cm

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rectangle area = L * 8 = 112, so L = 14. Perimeter = 2 * (14 + 8) = 44. Circumference = 132 - 44 = 88. 2 * pi * r = 88, so r = 88 / (2 * 22/7) = 14. Area of circle = pi * r^2 = (22/7) * 14 * 14 = 616.

AI explanation

Given the rectangle area is 112 sq. cm and its breadth is 8 cm, the length is 112 / 8 = 14 cm. The perimeter of the rectangle is 2 * (14 + 8) = 44 cm. With the total sum of perimeters being 132 cm, the circumference of the circle is 132 - 44 = 88 cm. Using the circumference formula 2 * pi * r = 88, we find the radius r = 14 cm. The area of the circle is pi * r^2 = (22/7) * 14 * 14 = 616 sq. cm.