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if the perimeter of a semicircle protractor is 36 cm find the diameter
Answers
Answer:
A.14 cm
Step-by-step explanation:
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Questions & Answers
CBSE
Mathematics
Grade 10
Parts of a Circle
Question
Answers
Related Questions
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
Answer
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Hint: As we all know that the perimeter of a circle is 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= 2radius(R)ofsemi−circle
The perimeter of the semi-circle = π R + D
⇒π R + D = π R + 2R⇒R(2 + π )
It is given that
Perimeter of semi-circle=36 cm
⇒R(2 + π ) = 36∴R = 362 + π
Putting the value of π = 227 , we get
⇒R = 362 + 227
On simplification we get,
⇒R = 36(7)14 + 22
⇒R = 36 × 736∴R = 7
Since, Diameter(D) of semi-circle= 2radius(R)ofsemi−circle
D = 2R = 2(7) = 14cm
Therefore, (D) 14 cm is the correct answer.
Answer:
Let r be the radius of the protractor, then
Perimeter = πr + 2r
According to the question,
36 = πr + 2r
⇒ 36 = r(22/7 + 2)
⇒ r = 7 cm.
∴ The diameter of the protractor is (2 × 7) cm = 14 cm.