Paper 1 · Mathematical Reasoning and Aptitude
UGC NET December 2023 (13.12.2023) Shift-II
A circle has the diameter equal to the length of the side of an equilateral triangle. What is the ratio of their respective areas?
A11 : 7 root 3
B22 : 7 root 3 ✓ Correct
C11 : 7 by root 3
D11 : root 3 by 3
Correct answer: (B) 22 : 7 root 3 — The ratio of the areas is 22 to 7 root 3, so that is the answer.
Explanation
★The ratio of the areas is 22 to 7 root 3, so that is the answer.
★Let the side of the equilateral triangle be a, which is also the circle's diameter.
★The circle's radius is a over 2, so its area is pi times a squared over 4.
★The equilateral triangle's area is root 3 over 4 times a squared.
★Dividing gives pi over root 3.
★Taking pi as 22 over 7, the ratio becomes 22 to 7 root 3.
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