Example 1
The cost of fencing a circular field at the rate of Rs 24 per metre is Rs 5280. The field is to be ploughed at the rate of Rs 0.50 per m2 . Find the cost of ploughing the field (Take π = 22/7 ).
Total cost of fencing a circular field = Rs 5280
Cost of fencing per meter = Rs 24
So, total length of field = (𝑇𝑜𝑡𝑎𝑙 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑓𝑒𝑛𝑐𝑖𝑛𝑔 )/(𝑐𝑜𝑠𝑡 𝑜𝑓 𝑓𝑒𝑛𝑐𝑖𝑛𝑔 𝑝𝑒𝑟 𝑚𝑒𝑡𝑒𝑟)
= 5280/24
= 220 m
Here,
Total length of the field would be circumference of the circular field .
Total length = circumference of circular field
220 = 2πr
2πr = 220
2 ×22/7× r= 220
(44 × r)/7 = 220
r = (220 × 7)/44
r = 35 m
Now,
Area of circular field = πr2
= 22/7×(35)2
= 22/7×35×35
= 22 × 5 ×35 m2
= 3850 m2
Now,
Cost of ploughing 1m2 of the Field = Rs 0.50
Cost of ploughing 3850 m2 of the Field = Rs 0.50 × 3850
= 1/2 × 3850
Rs 1925
Hence, Cost of ploughing the field = Rs 1925

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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