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Question
The diameter and length of a roller is 120 cm and 84 cm respectively. To level the ground, 200 rotations of the roller are required. Find the expenditure to level the ground at the rate of Rs. 10 per sq.m.
Solution
Radius of the roller, r = \[\frac{120}{2}\] = 60 cm
Length of the roller, h = 84 cm
Area of the ground levelled in one rotation of the roller = Curved surface area of the roller = \[2\pi r h = 2 \times \frac{22}{7} \times 60 \times 84\] = 31680 cm2
∴ Area of the ground levelled in 200 rotations of the roller
= 200 × Area of the ground levelled in one rotation of the roller
= 200 × 31680
= 6336000 cm2
= \[\frac{6336000}{10000}\] (1 m2 = 10000 cm2)
= 633.6 m2
Rate to level the ground = Rs 10/m2
∴ Expenditure (or total cost) to level the ground
= Total area of the ground × Rate to level the ground
= Area of the ground levelled in 200 rotations of the roller × Rate to level the ground
= 633.6 × 10
= Rs 6,336
Thus, the expenditure to level the ground is Rs 6,336.
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