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    if the perimeter of a semicircular protractor is 36 cm then its diameter is

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    If the perimeter of a semicircular protractor is 36 cm , then its diameter is :

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    Question

    If the perimeter of a semicircular protractor is 36cm, then its diameter is :

    A

    10cm

    B

    12cm

    C

    14cm

    D

    15cm

    Medium Open in App Solution Verified by Toppr

    Correct option is C)

    Perimeter of semicircular protractor=36 cm

    πr+2r=36 ⇒(π+2)r=36 ⇒( 7 22 ​ +2)r=36 ⇒ 7 36 ​ r=36 ⇒r= 36 36×7 ​ ⇒r=7

    Therefore, diameter =2r=2×7=14 cm

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    If the Perimeter of a Semi Circular Protractor is 36 Cm. Find Its Diameter.

    If the Perimeter of a Semi Circular Protractor is 36 Cm. Find Its Diameter.

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    If the perimeter of a semi-circular protractor is 36 cm. Find its diameter.

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    SOLUTION

    Let r cm be the radius of the protractor, then

    Perimeter = πr + 2r

    According to the question,

    ⇒ 36 = πr + 2r ⇒ 36 = r (227+2) ⇒ r = 7 cm.

    ∴ The diameter of the protractor is ( 2 x 7) cm = 14 cm.

    Concept: Circumference of a Circle

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    Chapter 17: Mensuration - Exercise 1

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    Chapter 17 Mensuration

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    If the perimeter of a semi

    If the perimeter of a semi-circle is 36 cm. what will be its diameter?A. 88 cmB. 22 cmC. 28 cmD. 14 cm. Ans: Hint: As we all know that the perimeter of a circle is \\[2\\pi R\\] where ‘R’ is the radius of the circle. Similarly, the perimeter of a sem...

    If the perimeter of a semi-circle is 36 cm. what will be its diameter?

    A. 88 cm B. 22 cm C. 28 cm D. 14 cm

    Last updated date: 19th Jan 2023

    • Total views: 255k • Views today: 5.51k Answer Verified 255k+ views

    Hint: As we all know that the perimeter of a circle is

    2πR 2πR

    where ‘R’ is the radius of the circle. Similarly, the perimeter of a semi-circle is half the perimeter of the circle with the addition of a length of the diameter which twice as the radius. With consideration of all these points, we’ll form an equation in ‘R’ to find its value and further to get the value of diameter.

    Complete step by step answer:

    Given data: Perimeter of semi-circle=36 cm.

    Using Diameter(D) of semi-circle= 2

    radius(R)ofsemi−circle

    radius(R)ofsemi−circle

    The perimeter of the semi-circle

    = π R + D = π R + D ⇒π R + D = π R + 2R ⇒R(2 + π )

    ⇒π R + D = π R + 2R⇒R(2 + π )

    It is given that

    Perimeter of semi-circle=36 cm

    ⇒R(2 + π ) = 36 ∴R = 36 2 + π

    ⇒R(2 + π ) = 36∴R = 362 + π

    Putting the value of

    π = 22 7 π = 227 , we get ⇒R = 36 2 + 22 7 ⇒R = 362 + 227

    On simplification we get,

    ⇒R = 36(7) 14 + 22 ⇒R = 36(7)14 + 22 ⇒R = 36 × 7 36 ∴R = 7 ⇒R = 36 × 736∴R = 7

    Since, Diameter(D) of semi-circle= 2

    radius(R)ofsemi−circle

    radius(R)ofsemi−circle

    D = 2R = 2(7) = 14cm

    D = 2R = 2(7) = 14cm

    Therefore, (D) 14 cm is the correct answer.

    Note: We can approach the answer using the formula for the perimeter as

    The perimeter of the semi-circle

    = π D 2 + D = π D2 + D π D 2 + D = D(1 + π 2 )

    π D2 + D = D(1 + π 2)

    It is given that

    Perimeter of semi-circle=36 cm

    D(1 + π 2 ) = 36 ⇒D = 36 1 + π 2

    D(1 + π 2) = 36⇒D = 361 + π 2

    Putting the value of

    π = 22 7 π = 227 , we get D = 36 1 + 11 7 ⇒D = 36 × 7 18 ⇒D = 2 × 7 ∴D = 14

    D = 361 + 117⇒D = 36 × 718⇒D = 2 × 7∴D = 14

    Therefore, Diameter of semi-circle= 14 cm

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