A circular road runs rounds a circular ground. If the difference between the circumference of the outer circle and the inner circle is 66 meters, the width of the road is?

Distance travelled in 1 revolution = circumference of the wheel
= ?d
= ( 22/7 ) x 63
= 198 cm

So the distance travelled in 100 revolutions = 100 x distance travelled in 1 revolution
= 100 x 198 cm
= 19800 cm
= 198 m

Distance covered in one revolution = total distance travelled / total number of revolution.
= ( 88 x 1000) / 1000 m
= 88 m

We know that the distance covered in one revolution = circumference of the wheel.
? ?d = 88
? 22d / 7 = 88
? d = 28 m

Number of round = total distance / circumference of wheel.
= (4 x 1000) / ?d
= (4 x 1000) / ( 22/7 x 7/11)
= 2000

Area = ?r² = 0.49?
? r = 0.7 m

Number of revolutions = total distance / circumference
= (1.76 x 1000) / (2 x 22/7 x 0.7)
= 400

Circumference = 2?r
= 2 x (22 / 7) x 70 cm
= 440 cm

Distance travelled in 10 revolutions = 440 x 10 cm
= 4400 cm
= 44 m

? Speed = distance / time
= 44 / 5 m/sec
= (44 / 5) x (18 / 5) km/hr
= 31.68 km/hr

Circumference of a circular = 2?r
? 2 x (22 / 7) x r = 440
? r = [440 x (7/22) x (1/2)] = 70 m

? Radius of outer circle = (70 + 14) m
= 84 m

The Radio of areas = area of first circle : area of 2nd circle
= ?r² / ?(3r)²
= ?r²/ 9 ?r²
= 1/9
= 1: 9

Area = (Diagonal)² / 2 = 50
? Diagonal = 10 units
? Radius of required circle = 5 units

Its area = [? x (5)² ] cm²
= 25? units²

Perimeter of rectangle = Circumference of circle
= 2?r
=2 x ( 22/7 ) x 42
= 264 cm

Now perimeter of rectangle = 2 x ( 6a + 5a )
? 2 x (6a + 5a) = 264
? a = 12

Smaller side of rectangle = 5a
= 60 cm

Circumference of circular plot= 88 m
? 2 x (22/7) x r = 88
? r = 88 x (7/22) x (1/2) = 14 m

Now area = ?r²
=( 22/7) x 14 x 14 m²
= 616 m²