Multiple choice

From a circular sheet of paper with radius 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the area of the uncut portion to that of the cut portion?

  1. 1 : 3

  2. 4 : 1

  3. 3 : 1

  4. 4 : 3
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C Correct answer
Explanation

Area of large circle = pi * 20^2 = 400pi. Area of 4 small circles = 4 * (pi * 5^2) = 4 * 25pi = 100pi. Uncut area = 400pi - 100pi = 300pi. Ratio of uncut to cut = 300pi : 100pi = 3 : 1.

AI explanation

The area of the original circular sheet is pi * 20^2 = 400*pi. The total area of the four cut-out circles is 4 * pi * 5^2 = 100*pi. The area of the uncut portion is 400*pi - 100*pi = 300*pi, making the ratio of the uncut portion to the cut portion 300*pi to 100*pi. The result is 3 : 1.

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