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 ___ .

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.