Nine times the area of a circle is same as the three times the area of a square. What is the ratio of the diameter of the circle and diagonal of the square?

This question was previously asked in
SSC MTS (2022) Official Paper (Held On: 16 May, 2023 Shift 2)
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  1.  ∶ 
  2. 2 ∶ 
  3. 2 ∶ 3π
  4.  ∶ 

Answer (Detailed Solution Below)

Option 1 :  ∶ 
Free
SSC MTS 2024 Official Paper (Held On: 01 Oct, 2024 Shift 1)
90 Qs. 150 Marks 90 Mins

Detailed Solution

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Given:

Nine times the area of a circle is the same as the three times the area of a square.

Formula used:

Area of a circle = πr2 (r = radius)

Diameter = 2 × radius

Area of a square = a2. (a is the side of the square)

The diagonal of the square = a√2

Calculation:

As per the question,

9πr= 3 a2

⇒ 3πr2 =  a2

  =  a/r

⇒  2r / a√2  = √2 : 

The correct option is 1

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