A brooch is a small piece of jewellery which has a pin at the back so it can be fastened on a dress, blouse or coat. Designs of some brooch are shown below. Observe them carefully.

Design A:
Brooch A is made with silver wire in the form of a circle with diameter 28mm. The wire used for making 4 diameters which divide the circle into 8 equal parts.

Design B:
Brooch b is made two colours_Gold and silver. Outer part is made with Gold. The circumference of silver part is 44mm and the gold part is 3mm wide everywhere.

Refer to Design A

Question 1

The total length of silver wire required is

(a) 180 mm (b) 200 mm

(c) 250 mm (d) 280 mm

Question 2

The area of each sector of the brooch is

(a) 44 mm
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2
}
(b) 52 mm
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2
}

(c) 77 mm
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2
}
(d) 68 mm
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2
}

Refer Design B:

Question 3

The circumference of outer part (golden) is

(a) 48.49 mm (b) 82.2 mm

(c) 72.50 mm (d) 62.86 mm

Question 4

The difference of areas of golden and silver parts is

(a) 18 π (b) 44 π

(c) 51 π (d) 64 π

Question 5

A boy is playing with brooch B. He makes revolution with it along its edge. How many complete revolutions must it take to cover 80 π mm?

Question A brooch is a small piece of jewellery which has a pin at the back so it can be fastened on a dress, blouse or coat. Designs of some brooch are shown below. Observe them carefully. Design A: Brooch A is made with silver wire in the form of a circle with diameter 28mm. The wire used for making 4 diameters which divide the circle into 8 equal parts. Design B: Brooch b is made two colours_Gold and silver. Outer part is made with Gold. The circumference of silver part is 44mm and the gold part is 3mm wide everywhere.Refer to Design A Question 1 The total length of silver wire required is (a) 180 mm (b) 200 mm (c) 250 mm (d) 280 mmTotal wire is used
= Length of wire in Circle
+ Wire used in 4 diameters
Now,
Diameter of the brooch = 28 mm
Radius of brooch = 28/2 = 14 mm
Length of wire in circle
Length of wire in circle = Circumference of Circle
= 2𝜋𝑟
= 2×22/7× 14
= 2 × 22 × 2
= 88 mm
Silver wire used in 4 diameters = 4 × Diameter of circle
= 4 × 28
= 112 mm
Now,
Total wire is used = length of wire in circle + Wire used in 5 diameters
= 88 + 112
= 200 mm
So, the correct answer is (b)
Length of wire in circle = Circumference of Circle
= 2𝜋𝑟
= 2×22/7× 14
= 2 × 22 × 2
= 88 mm
Silver wire used in 4 diameters = 4 × Diameter of circle
= 4 × 28
= 112 mm
Now,
Total wire is used = Length of wire in circle + Wire used in 4 diameters
= 88 + 112
= 200 mm
So, the correct answer is (b)
Question 2 The area of each sector of the brooch is (a) 44 mm2 (b) 52 mm2 (c) 77 mm2 (d) 68 mm2Since the wire divides the circle into 8 equal sectors
Area of each sector of the brooch
= 1/8× Area of all sectors of the brooch
= 𝟏/𝟖× Area of circle
= 1/8× 𝜋𝑟2
= 1/8× 22/7×(14)^2
= 1/8× 22/7×14 × 14
= 11 × 1 × 7
= 77 mm2
So, the correct answer is (c)
Refer Design B: Question 3 The circumference of outer part (golden) is (a) 48.49 mm (b) 82.2 mm (c) 72.50 mm (d) 62.86 mmGiven that
Circumference of silver part is 44mm
2𝜋r = 44
2 × 22/7 × r = 44
44/7 × r = 44
r = 44 × 7/44
r = 7 mm
Thus,
Radius of golden + sliver part = 7 + 3 = 10 mm
Now,
Circumference of Golden part = 2𝜋 × Radius of (golden + silver) part
= 2 × 22/7 × 10
= 2 × 3.143 × 10
= 6.286 × 10
= 62.86 mm
So, the correct answer is (d)
Thus,
Radius of golden + sliver part = 7 + 3 = 10 mm
Now,
Circumference of Golden part
= 2𝜋 × Radius of (golden + silver) part
= 2 × 22/7 × 10
= 2 × 3.143 × 10
= 6.286 × 10
= 62.86 mm
So, the correct answer is (d)
Question 4 The difference of areas of golden and silver parts is (a) 18 𝜋 (b) 44 𝜋 (c) 51 𝜋 (d) 64 𝜋
Difference b/w areas of golden and silver part
= Area of silver − Area of golden
= Area of circle of radius 10mm − Area of circle of radius 7mm
= 𝜋(10)2 − 𝜋(7)2
= 100𝜋 − 49𝜋
= 51 𝜋
So, the correct answer is (c)
Question 5 A boy is playing with brooch B. He makes revolution with it along its edge. How many complete revolutions must it take to cover 80 𝜋 mm? (a) 2 (b) 3 (c) 4 (d) 5Here,
Number of revolutions = (𝑻𝒐𝒕𝒂𝒍 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆)/(𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒄𝒐𝒗𝒆𝒓𝒆𝒅 𝒊𝒏 𝟏 𝒓𝒆𝒗𝒐𝒍𝒖𝒕𝒊𝒐𝒏)
Radius of Brooch B = 10 cm
Therefore,
Distance covered in one revolution = Circumference of wheel
= 2𝜋r
= 2 × 𝜋 × 10
= 20𝜋 mm
Now,
Number of revolutions = (𝑇𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒)/(𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑐𝑜𝑣𝑒𝑟𝑒𝑑 𝑖𝑛 1 𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛)
= 80𝜋/20π
= 4
So, the correct answer is (c)

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.