Multiple choice

The total area of a circle and a rectangle is equal to 1166 sq.cm. If the length of the rectangle is 25 cm and the diameter of the circle is 28 cm, what is the sum of the circumference of the circle and the perimeter of the rectangle?

  1. 180 cm

  2. 182 cm

  3. 184 cm

  4. 186 cm

  5. 191 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Area of circle = pi * r^2 = 22/7 * 14 * 14 = 616. Area of rectangle = 1166 - 616 = 550. Length = 25, so width = 550 / 25 = 22. Circumference = 2 * 22/7 * 14 = 88. Perimeter = 2 * (25 + 22) = 94. Sum = 88 + 94 = 182.

AI explanation

Using the circle area formula with the given diameter of 28 centimetres, the area is 22 over 7 times 14 squared, which equals 616 square centimetres. Subtracting this from the total area of 1166 square centimetres leaves 550 square centimetres for the rectangle, and dividing by the length of 25 centimetres gives a width of 22 centimetres. The circumference of the circle is 22 over 7 times 28, or 88 centimetres, and the perimeter of the rectangle is 2 times the sum of 25 and 22, or 94 centimetres, making the total sum 182 centimetres.

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