Question

A brooch is crafted from silver wire in the shape of a circle with a diameter of 35 cm. The wire is also used to create 5 diameters, dividing the circle into 10 equal sectors as shown in figure.

Based on the above information, answer the following questions:

1. What is the radius of circle?   1
2. What is the circumference of the brooch?   1
3. 1. What is the total length of silver wire required?  2
      OR
   2. What is the area of each sector of the brooch?  2

Answer 1

Given: d = 35 cm

(i) The radius is half of the diameter (d).

r = `d/2`

= `35/2`

= 17.5 cm

(ii) The circumference (C) of brooch = πd    ...(Taking`pi = 22/7`)

= `22/7 xx 35` 

= 22 × 5

= 110 cm

(iii) (a) The wire is used for the outer circumference plus the 5 internal diameters. 

Total length = 110 + (5 × 35)

= 110 + 175

= 285 cm

OR

(b) The circle is divided into 10 equal sectors.

Area of 1 sector = `"Total area of circle"/10`

Total area of square = πr²

= `22/7 xx 17.5 xx 17.5`

= `22/7 xx 306.25`

= 22 × 43.75

= 962.5 cm²

Now, divide by 10 for one sector:

Area of each sector = `962.5/10`

= 96.25 cm²