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
^{
2
}
(b) 52 mm
^{
2
}

(c) 77 mm
^{
2
}
(d) 68 mm
^{
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?

(a) 2 (b) 3 (c) 4 (d) 5

Transcript

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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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