The cost of ploughing a circular field at the rate of Rs 0.75 per m2

1.	The cost of ploughing a circular field at the rate of Rs 0.75 per m2 is Rs.4158. Find the cost of fencing the field at the rate of Rs.30 per metre.
Answer» Let radius of circular field be rm. ∴ Area of circular field is π r²m². ∴ Cost of ploughing circular field at the rate of Rs 0.75 per m² = πr²x Rs 0.75 = Rs (3/4 πr²)m² ∴ 3/4 πr²= 4158 (∵ Given cost = Rs 4158) = r² = 4158 x 4/3 x 7/22 ( ∵ π = 22/7) = r² = 63 x 4 x 7 = 9 x 7 x 4 x7 = 3² x 2² x 7² = (3x2x7)² = 42² = r = 42 m ∴ Perimeter of circular field is P = 2 πr = 2 x 22/7 x 42 = 264 m ∴ Cost of fencing the field = Rs 30 per meter ∴ Cost of fencing the circular field = Rs (264 x 30) = Rs 7920

The cost of ploughing a circular field at the rate of Rs 0.75 per m2 is Rs.4158. Find the cost of fencing the field at the rate of Rs.30 per metre.

Answer»

Let radius of circular field be rm.

∴ Area of circular field is π r²m².

∴ Cost of ploughing circular field at the rate of Rs 0.75 per

m² = πr²x Rs 0.75 = Rs (3/4 πr²)m²

∴ 3/4 πr²= 4158 (∵ Given cost = Rs 4158)

= r² = 4158 x 4/3 x 7/22 ( ∵ π = 22/7)

= r² = 63 x 4 x 7

= 9 x 7 x 4 x7

= 3² x 2² x 7²

= (3x2x7)²

= 42²

= r = 42 m

∴ Perimeter of circular field is P = 2 πr

= 2 x 22/7 x 42 = 264 m

∴ Cost of fencing the field = Rs 30 per meter

∴ Cost of fencing the circular field

= Rs (264 x 30)

= Rs 7920

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