Question

The figure below shows a circle divided into 3 equal parts. The shaded region corresponds to $(\frac{2}{3}{)}^{rd}$ of the circle. If the unshaded region corresponds to $(\frac{a}{3}{)}^{rd}$ of the circle. Then, the value of a is _____.

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Answer 1

Since the entire circle is divided into 3 equal parts, each part represents ${\frac{1}{3}}^{rd}$ of the circle. Since there are two shaded parts, the shaded region corresponds to ${\frac{2}{3}}^{rd}$ of the circle. There is only one part which is unshaded and hence this corresponds to ${\frac{1}{3}}^{rd}$ of the circle.

Therefore a = 1.