A circle has the diameter same as the length of the side of an equilateral…
2023
A circle has the diameter same as the length of the side of an equilateral triangle. What is the ratio of their respective areas?
- A.
11 : 7√3
- B.
22 : 7√3
- C.
11 : 14/√3
- D.
11 : 7/√3
Attempted by 3 students.
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Correct answer: B
Let s be the side length of the equilateral triangle.
The circle's diameter equals s, so its radius is s/2. Circle area = π(s/2)² = (πs²)/4.
Triangle area = (√3/4)s².
Ratio of areas = [(πs²)/4] / [(√3/4)s²] = π/√3.
Approximating π as 22/7, the ratio is 22/(7√3).