1. b) 200 mm
![](https://www.sarthaks.com/?qa=blob&qa_blobid=3317853681560529230)
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
![](https://www.sarthaks.com/?qa=blob&qa_blobid=12399854214206985256)
![](https://www.sarthaks.com/?qa=blob&qa_blobid=2220461634801708611)
3. d) 62.86 mm
![](https://www.sarthaks.com/?qa=blob&qa_blobid=17143737877026017477)
Given that
Circumference of silver part is 44
![](https://www.sarthaks.com/?qa=blob&qa_blobid=8033319689765502253)
Thus,
Radius of golden + silver part = 7 + 3 = 10 mm
![](https://www.sarthaks.com/?qa=blob&qa_blobid=13243673651925859133)
Circumference of Golden part
= 2π x Radius of (golden + silver) part
![](https://www.sarthaks.com/?qa=blob&qa_blobid=6600089031358115748)
4. c) 51π
![](https://www.sarthaks.com/?qa=blob&qa_blobid=3186994674766958421)
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
![](https://www.sarthaks.com/?qa=blob&qa_blobid=8220653372323157322)
Radius of Brooch B = 10 cm
Therefore,
Distance covered in one revolution = Circumference of wheel
= 2πr
= 2 x π x 10
= 20π mm
Now,
![](https://www.sarthaks.com/?qa=blob&qa_blobid=13454211391904354017)