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

1. The total length of silver wire required is

a) 180 mm

b) 200 mm

c) 250 mm

d) 280 mm

2. The area of each sector of the brooch is

a) 44 mm²

b) 52 mm²

c) 77 mm²

d) 68 mm²

Refer to Design B

3. The circumference of outer part (golden) is

a) 48.49 mm

b) 82.2 mm

c) 72.50 mm

d) 62.86 mm

4. The difference of areas of golden and silver parts is

a) 18 π 

b) 44 π 

c) 51 π 

d) 64 π 

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

Answer 1

1. b) 200 mm

Total 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 = Circumference of Circle

= 2πr

= 2x 22 x 14

= 2 × 22 × 2

= 88 mm

Silver wire used in 4 diameters = 4 x 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

2. c) 77mm²

Since the wire divides the circle into 8 equal sectors

Area of each sector of the brooch

3. d) 62.86 mm

Given that

Circumference of silver part is 44

Thus,

Radius of golden + silver part = 7 + 3 = 10 mm

Circumference of Golden part

= 2π x Radius of (golden + silver) part

4. c) 51π

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

= 51π

5. c) 4

Radius of Brooch B = 10 cm

Therefore,

Distance covered in one revolution = Circumference of wheel

= 2πr

= 2 x π x 10

= 20π mm

Now,

Answer 2

1. b) 200 mm

2. c) 77m m²

3. d) 62.86 mm

4. c) 51 π 

5. c) 4