PYQ Vault

Wire re-bent from one shape into another: find the new side, radius or area

This type of question, asked 6 times: CDS 1 2017, CDS 1 2018, CDS 1 2019, CDS 1 2021, CDS 1 2022, CDS 2 2025. All 7 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 1 2017

    83
    A copper wire when bent in the form of a square encloses an area of 121 cm2121 \text{ cm}^2. If the same wire is bent in the form of a circle, it encloses an area equal to

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  2. Question 2

    CDS 1 2018

    94
    A square and an equilateral triangle have the same perimeter. If the diagonal of the square is 626\sqrt{2} cm, then what is the area of the triangle ?

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  3. Question 3

    CDS 1 2018

    88
    A wire is in the form of a circle of radius 98 cm. A square is formed out of the wire. What is the length of a side of the square ? (Use π=22/7\pi = 22/7)

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  4. Question 4

    CDS 1 2019

    43
    A piece of wire is in the form of a sector of a circle of radius 20 cm, subtending an angle 150∘150^\circ at the centre. If it is bent in the form of a circle, then what will be its radius ?

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  5. Question 5

    CDS 1 2021

    74
    A wire is in the form of a circle of radius 70 cm. If it is bent in the form of a rhombus, then what is its side length? (Take π=227\pi = \frac{22}{7})

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  6. Question 6

    CDS 1 2022

    76
    The diagonal of a square is 12212\sqrt{2} cm and the area of an equilateral triangle is 64364\sqrt{3} square cm. Which of the following statements is/are correct? 1. The square and the triangle have the same perimeter. 2. Four times the area of the square is equal to 333\sqrt{3} times the area of the triangle. Select the correct answer using the code given below.

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  7. Question 7

    CDS 2 2025

    79
    A wire is in the form of an equilateral triangle with an area of 36336\sqrt{3} cm2^2. If it is changed into a semicircle, then what is its radius?

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