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Example 23: A road roller takes 250 complete revolutions to level a tarred road. Find the area of
the road if the diameter of the road roller is 70 cm and the length is 1 m.

Solution: We have, the diameter of the road roller, 2r = 70 cm
70
Therefore, r = cm = 35 cm
2
Also, the length of the road roller, h = 1 m = 100 cm.
Considering the road roller as a cylinder, we will find the area of the levelled road.

Area of the road levelled by the road roller in one revolution = Curved surface area of the road roller

= 2prh
22
2
= 2 × × 35 100 cm = 22000 cm 2
×
7
Area of the road levelled by the road roller in 250 complete revolutions
2
= 22000 × 250 cm = 5500000 cm 2
5500000
2
2
2
= m = 550 m [Q 1 m = 100 cm × 100 cm = 10000 cm ]
2
10000
Example 24: The lateral surface area of a hollow cylinder is 3080 cm . A rectangular sheet of width
2
44 cm is formed when it is cut along its height. Find the length of the rectangular sheet.
Solution: When the hollow cylinder is cut along its height, it will take the shape of a rectangle whose
width (b) = 44 cm, and length (l) = height (h) of the cylinder will be equal to the circumference of
the base (or top) circle = 2πr
i.e., h = 44 cm …(i)
Also, it is given that the lateral surface area of the hollow cylinder = 3080 cm 2

⇒ 2πrh = 3080 cm 2

Putting h = 44 cm from (i), we get
44 cm × 2πr = 3080 cm 2 44 cm
3080
2πr = cm = 70 cm
44
Thus, the length of the rectangular sheet is 70 cm.

Example 25: A horse stable is in the form of a cuboid, whose external dimensions are
70 m × 35 m × 40 m is mounted by a semi-cylinder vertically on the top. The cuboid is also open
from the front face. Find the cost of painting the exterior of the stable at the rate of `2/m .
2
Solution: The horse stable as described above can be represented by Semi-cylinder roof
of 35 m diameter
the adjoining diagram. 5 3

The area that needs to be painted is as follows: 4
6 1
Area to be painted = Three walls of stable 70 m 35 m
+ Curved surface of semi-cylindrical 40 m Stable open from 2
this side (Front)
roof

+ Side walls of semi-cylindrical roof

247 Mensuration