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    Question

    If the perimeter of a circle is equal to that of a square, then the ratio of their areas is

    A

    22:7

    B

    14:11

    C

    7:22

    D

    11:14

    Medium Open in App Solution Verified by Toppr

    Correct option is B)

    Step -1: Equate perimeter of a square and circle.

    Let r be the radius of a circle

    and be the side of a square.

    From the given data,

    Perimeter of a square = Circumference of a circle

    ⇒4a=2πr ⇒ r a ​ = 2 π ​ …(1)

    Step -2: Calculate the ratio of area of square and circle.

    Area of circle:Area of square

    ⇒ Area of square Area of circle ​ = a 2 πr 2 ​ ⇒ Area of square Area of circle ​ =π( a r ​ ) 2 ⇒ Area of square Area of circle ​ =π( π 2 ​ ) 2 (From equation (1)) ⇒ Area of square Area of circle ​ =π π 2 4 ​ ⇒ Area of square Area of circle ​ = π 4 ​ ⇒ Area of square Area of circle ​ = 22 4×7 ​ (∵π= 7 22 ​ ) ⇒ Area of square Area of circle ​ = 11 14 ​

    Hence, option (B) 14:11 is correct answer.

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    [Solved] If the perimeter of a circle and a square are equal, then wh

    Given:  The perimeter of the circle is equal to that of the square. Formula: If “r” is the radius of the circle and a” is the sid

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    If the perimeter of a circle and a square are equal, then what is the ratio of the area of the circle to that of the square?

    This question was previously asked in

    CDS Maths Previous Paper 10 (Held On: 8 Nov 2020) - 10

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    1 ∶ π 2 ∶ π 3 ∶ π 4 ∶ π

    Answer (Detailed Solution Below)

    Option 4 : 4 ∶ π

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    Detailed Solution

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    Given: 

    The perimeter of the circle is equal to that of the square.

    Formula:

    If “r” is the radius of the circle and a” is the side of the square,

    1) Perimeter of a circle = 2πr

    2) Area of a circle = πr2

    3) Perimeter of a square = 4a

    4) Area of a square = a2

    Calculation:

    Let “r” be the radius of the circle and “a” be the side of the square,

    According to the question,

    The perimeter of the circle is equal to that of the square.

    2πr = 4a

    ⇒ r/a = 4/(2π) = 2/π      ----(1)

    Now, the ratio of the area of circle and Area of square:

    ⇒ πr2/a2      ----(2)

    From equation (1) and (2),

    πr2/a2 = π(2/π)2 ⇒ πr2/a2 = 4/π

    ∴ The ratio of the area of a circle to that of a square is 4 ∶ π.

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    स्रोत : testbook.com

    If the perimeter of a circle is equal to that of a square, then the ratio of their areas is ______.

    If the perimeter of a circle is equal to that of a square, then the ratio of their areas is ______.

    Advertisement Remove all ads MCQ Fill in the Blanks

    If the perimeter of a circle is equal to that of a square, then the ratio of their areas is ______.

    OPTIONS

    13 : 22 14 : 11 22 : 13 11 : 14 Advertisement Remove all ads

    SOLUTION

    If the perimeter of a circle is equal to that of a square, then the ratio of their areas is 14 : 11.

    Explanation:

    Let radius of circle be r and side of a square be a.

    Perimeter of a circle = Perimeter of a square

    ∴ 2πr=4a ⇒ a=πr2 .....(i) Now, Area of circle Area of square

    Area of circleArea of square=πr2(a)2=π2(πr2)2

    ......[From equation (i)]

    = πr2π2r24=4π = 4227=2822 = 1411

    Concept: Area of Circle

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    Chapter 13: Areas Related to Circles - Exercise 13.6 [Page 73]

    Q 39 Q 38 Q 40

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    RD Sharma Class 10 Maths

    Chapter 13 Areas Related to Circles

    Exercise 13.6 | Q 39 | Page 73

    NCERT Mathematics Exemplar Class 10

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    Area of Circle video tutorial 02:30:15 Advertisement Remove all ads

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