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

Q 2 Q 1 Q 3

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ICSE Class 10 Mathematics

Chapter 17 Mensuration

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Circumference of a Circle

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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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