Multiple choice

The total area of a circle and a square is 2611 sq. cm. The diameter of the circle is 42 cm. What is the sum of the circumference of the circle and the perimeter of the square?

  1. 272 cm

  2. 380 cm

  3. 280 cm

  4. 294 cm

  5. 270 cm
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A Correct answer
Explanation

Diameter = 42, Radius = 21. Area of circle = (22/7) * 21 * 21 = 1386. Area of square = 2611 - 1386 = 1225. Side of square = sqrt(1225) = 35. Circumference of circle = 2 * (22/7) * 21 = 132. Perimeter of square = 4 * 35 = 140. Sum = 132 + 140 = 272.

AI explanation

Using the given diameter of 42 cm, the radius of the circle is 21 cm, making its area pi*r^2 equal to (22/7)441 = 1386 sq. cm. Subtracting this from the total area gives the square's area as 2611 - 1386 = 1225 sq. cm, meaning its side is the square root of 1225, which is 35 cm. The circumference of the circle is 2*pi*r = 2(22/7)*21 = 132 cm, and the perimeter of the square is 4*35 = 140 cm, so their sum is 132 + 140 = 272 cm.

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