Page 249 - Start Up Mathematics_7

264 m 26400 cm
= = = 150
176 cm 176 cm
The wheel must rotate 150 times to cover 176 m.

Conversion of Units

The area of a region formed by a square of Length Area
side 1 cm is called a square centimetre and 1 cm = 10 mm 1 cm = 100 mm 2
2
2
written as 1 cm . The area of a square of 1 dm = 10 cm 1 dm = 100 cm 2
2
side 1 decametre (1 dam) is called an are 1 m = 10 dm 1 m = 100 dm 2
2
2
and written as 1 dam or 1 are. The area of a 1 dam = 10 m 1 m = 10,000 cm 2
2
region formed by a square of side 1 hectometre 2 2
2
(1 hm) is called a hectare, written as 1 hm . 1 hm = 10 dam 1 km = 10,00,000 m
It is also possible to convert length and area 1 km = 10 hm 1 are = 100 m 2
from one unit to the other. The following table 1 m = 100 cm 1 hectare = 10,000 m 2
is given for ready reference. 1 km = 1,000 m 1 hectare = 100 are

EXERCISE 14.3

1. Find the circumference of the circles, given that:

(a) radius = 21 mm (b) diameter = 14 cm

2. Find the area of the circles, given that: (a) radius = 20 cm (b) diameter = 42 cm
3. Find the radius of a circle whose circumference is 39.6 cm.

4. Find the ratio of the circumferences of two circles whose radii are in the ratio 4 : 5.
5. The inner circumference of a circular track is 176 m. The track is 7 m wide. Calculate the:

(a) area of the track.
(b) cost of putting up a fence along the outer circle at the rate of ` 12 per metre.
22
(Use π = 7 )
6. The circumference of a circle exceeds its radius by 37 cm. Find the diameter of the circle.

(Use π = 22 )
7
7. The diameter of a wheel of a bus is 112 cm. How many revolutions will it make to cover
1 km 56 metres?

8. The circumferences of two circles are in the ratio 1 : 3. Find the ratio of their areas.
9. A copper wire in the form of a circle, encloses an area of 616
2
cm . If the same wire is bent to form a square, find its area.
(Use π = 22 )
7
10. ABCD is a diameter of a circle of radius 6 cm. The lengths A B C D
AB, BC and CD are equal. Semicircles are drawn on AB and
BD as diameters as shown in the given figure. Find the area
of the shaded region.

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