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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.