QOTD - Quantitative Aptitude Problem - Mensuration


2019-08-22 | Team PendulumEdu

A rhombus is inscribed in a circle in such a way that one vertex of rhombus is on the center while other three vertices are on the circumference of the circle. If the radius of the circle is 4 m then, what will be the ratio of area of circle and rhombus?

Options:

Solution:

According to the information given in the question, the schematic will be

qotd-22-aug-2019-mensuration-quantative-pendulumedu

In the above figure,

OA = OC = OB = radius of circle

Since, the opposite sides of a rhombus are equal

Thus, OA = CB and OC = AB

So, from the above figure,

Area of rhombus OABC (AR) will be = area of triangle OAB + area of triangle OBC

Since, both are equilateral triangle, the area will be

 

Now, area of circle Ac will be

 

Therefore, the ratio of the area of circle to that of rhombus will be

Hence, (D) is the correct answer.

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