In a workshop, brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in the given figure.

Question 1

What is the radius of the circle?

(A) 35/2 mm (B) 5/2 mm

(C) 35 mm (C) 10 mm

Question 2

What is the circumference of the brooch?

(a) 100 mm (b) 110 mm

(c) 50 mm (d) 10 mm

Question 3

What is the total length of silver wire required?

(a) 528 mm (b) 825 mm

(c) 285 mm (d) 852 mm

Question 4

What is the area of the each sector of the brooch?

(A) 385/2 mm
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2
}
(B) 358/4 mm
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2
}

(C) 584/4 mm
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2
}
(D) 385/4 mm
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2
}

Question 5

The given problem is based on which mathematical concept?

Question In a workshop, brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in the given figure. Question 1 What is the radius of the circle? (A) 35/2 mm (B) 5/2 mm (C) 35 mm (C) 10 mm Given
Diameter = 35 mm
Thus,
Radius of circle = Diameter/2
= 𝟑𝟓/𝟐 mm
So, the correct answer is (A)
Question 2 What is the circumference of the brooch? (a) 100 mm (b) 110 mm (c) 50 mm (d) 10 mm Now,
Circumference of brooch = 2𝜋𝑟
= 2×22/7×35/2
= 110 mm
So, the correct answer is (B)
Question 3 What is the total length of silver wire required? (a) 528 mm (b) 825 mm (c) 285 mm (d) 852 mm vTotal wire is required
= Length of wire in circle + Wire used in 5 diameters
Now,
Length of wire in circle
= Circumference of Circle
= 110 mm
Also,
Silver wire used in 5 diameters = 5 × Diameter of circle
= 5 × 35
= 175 mm
Now,
Total wire is used = Length of wire in circle + Wire used in 5 diameters
= 110 + 175
= 285 mm
So, the correct answer is (C)
Question 4 What is the area of the each sector of the brooch? (A) 385/2 mm2 (B) 358/4 mm2 (C) 584/4 mm2 (D) 385/4 mm2 Since the wire divides the circle into 10 equal sectors
Area of each sector of the brooch
= 1/10× Area of all sectors of the brooch
= 𝟏/𝟏𝟎× Area of circle
= 1/10× 𝜋𝑟2
= 1/10× 22/7×(35/2)^2
= 1/10× 22/7×35/2 ×35/2
= 𝟑𝟖𝟓/𝟒 mm2
= 1/10× 22/7×35/2 ×35/2
= 𝟑𝟖𝟓/𝟒 mm2
So, the correct answer is (a)
Question 5 The given problem is based on which mathematical concept? (a) Areas Related to circles (b) Circles (c) Construction (d) none of these The given problem is based on Area related to circles
So, the correct answer is (a)

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.