Equal sized circular regions are shaded in a square sheet of paper of 1 cm side length. Two cases, case M and case N, are considered as shown in the figures below. In the case M, four circles are shaded in the square sheet and in the case N, nine circles are shaded in the square sheet as s

Question

Equal sized circular regions are shaded in a square sheet of paper of 1 cm side length. Two cases, case M and case N, are considered as shown in the figures below. In the case M, four circles are shaded in the square sheet and in the case N, nine circles are shaded in the square sheet as shown.

What is the ratio of the areas of unshaded regions of case M to that of case N?

Accepted Answer

1: 1. In both cases, the total area of the square is 1 cm². In case M, four circles are shaded, each with a radius of 0.25 cm, giving a total shaded area of 4 × (π × (0.25)²) = π cm². In case N, nine circles are shaded, each with a radius of approximately 0.333 cm, resulting in a total shaded area of 9 × (π × (0.333)²) = π cm² as well. Since both cases have the same shaded area, the unshaded areas are equal, leading to a ratio of 1:1.

Solution

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