Page 233 - ICSE Math 8

22
Whenever the value of π is not given, take π = .
7

2
Example 17: Find the circumference of a circle whose area is 1,386 cm .
Solution: Area of the circle = 1,386 cm 2
2
⇒ πr = 1,386
22 1,386 × 7
2
2
⇒ 7 × r = 1,386 ⇒ r = 22 ⇒ r = 441 ⇒ r = 21 cm
∴ Circumference of the circle = 2πr = 2 × 22 × 21 cm = 132 cm
7
2
Example 18: A metal wire is bent to form a square with area 1,936 cm . If the same wire is bent to form a
circle, find the area of the circle.
Solution: Let each side of the square be a cm.
2
2
Area of the square = 1,936 cm ⇒ a = 1,936 ⇒ a = 44
Perimeter of the square = 4a = 4 × 44 cm = 176 cm
Circumference of the circle = Perimeter of the square
⇒ 2πr = 176
22 176 × 7
⇒ 2 × 7 × r = 176 ⇒ r = 2 × 22 cm ⇒ r = 28 cm
22
2
2
∴ Area of the circle = πr = 7 × 28 × 28 cm = 2,464 cm 2
Example 19: Outside the boundary of a circular ground of radius 15 m, there is a circular path of uniform
width of 5 m. Find the area of the path. B
Solution: Radius (r) of the ground = 15 m
Radius (R) of the circular path = 15 m + 5 m = 20 m 20 m
Area of the path = Area of the circular path – Area of the ground O 15 m A
2
2
2
2
= π(R – r ) = π(20 – 15 )
22 5 m
2
2
= 7 × (20 + 15)(20 – 15) [Using a – b = (a + b)(a – b)]
22
= 7 × 35 × 5 = 550 m 2
Example 20: A wheel of a bicycle of diameter 54 cm is making 35 revolutions in every 12 seconds. Find
–1
the speed of the bicycle in km h .
Solution: Diameter of the wheel = 54 cm Maths Info
∴ Radius = 27 cm Distance covered by a wheel
22 in one revolution is equal to its
Circumference of the wheel = 2πr = 2 × 7 × 27 cm circumference.
22
Distance covered in 35 revolutions in 12 s = 2 × 7 × 27 × 35 cm = 5,940 cm
5,940
Distance covered in 1 s = 12 cm

5,940 5,940 × 60 × 60
Distance covered in 1 h = 12 × 60 × 60 cm = 12 × 100 × 1,000 km

5,940 × 60 × 60  Distance 
–1
∴ Speed of bicycle = 1 × 12 × 100 × 1,000 km h   Speed = Time  
= 17.82 km h –1

221