Page 194 - classs 6 a_Neat

Circumference EXERCISE 14-C
You will find in each case that: = 3.14 (nearly )
Diameter

This ratio is denoted by 1t ( called pi). Circumference = π c = π ⇒ = c 2r 1. Find 28 the cm circumference of a 10.5 circle cm whose radius (iii) is

(ii) 10.5 cm

π ⇒

(i) 28 cm
(iii) 3.5 m
Diameter 2r distance covered by the wheel in 100 0revolution
Hence, circumference = 2nr units, where r is the radius of the circle. 2. Find 14 the cm circumference (ii) of 35 a cm circle whose diameter is
22 =(2.20x1000)m=2200
REMARK Unless stated, we take 1t =
7
EXAMPLE:1 Find the circumference of a circle of radius 14 cm. (i) 14 cm (ii) 35 cm (iii) 10.5m
SOLUTION The radius of the of given circle is r = 14 cm 3. Find the radius of a circle whose circumference is 1 76 cm.
∴circumference of the circle is given by 4. Find the diameter of a wheel whose circumference is 264 cm.
5. Find wheel the is 77 distance cm. covered by the wheel of a car in 500 -revolutions if the diameter of the
= c π = 2 r   × 2 22 × 14   =cm 88cm. 6. The diameter of the wheel of a car is 70 cm. How many revolutions will it make to travel 1.65 km?
 7 
Hence, the circumference of the given circle is 88 cm.

EXAMPLE:2 Find the diameter of a circle whose circumference is 66m
SOLUTION Let radius of the given circle be r cm.
Then its circumference= π2r cm.
66
r
r
∴2 π = 66 ⇒=
2 π
⇒=   × 7  66  cm = 21 cm = 10.5cm.
r
 22  2 2
Hence, the diameter of the circle is (2 x 10.5) cm= 21 cm.
Conversion of units:
Units of length Units of area
1 cm= 10 mm 1 cm = (10 × 10) mm =100 mm 2
2
2
1 m = 100 cm 1 m = (100 × 100) cm = 10,000 cm 2
2
2
1dm = 10cm 1 dm = (10 × 10) cm = 100 cm 2
2
2
1 dam= 10 m 1 dam = (10 × 10) m = 100 m 2
2
2
1 km= 10 hm 1 km = (10 × 10) hm = 100 hm 2
2
2
1 km= 1000 m 1 km = (10 × 10) hm = 1000000 m 2
2
2
Larger units of area
1 acre= 100 m 2 and 1 hectare= 10,000 m 2
100 acres= 1 hectare 1 00 hectares = 1 sq. km
EXAMPLE:3 The during the diameter time of in a which wheel of the a car wheel ts 70 makes cm.
1000 Find the revolutions. distance covered by the car
70
SOLUTION Radms . of the wheel cm = 35 cm
2
Circumference of the wheel= 2π r

=   2 × 22 × 35 cm = 22cm = 2.20 .
m

 7 
In revolution, the wheel covers a in distance equal to its circumference.
∴ distance covered by the wheel in 1 revolution =2.20m.
X∴ m = 2.2 km.