A gardener wants to fence a circular garden of diameter 21m.find the length of the wire he needs to purchase and cost of it at the rate of Rs.4 per meter.
Given, Diameter = 21m, cost of the rope = Rs 4 per meter, length of the rope required to fence the garden two round=?, Cost of the rope = ?
The length of rope required = 2 × circumference.
Circumference = 2 π r = π D
= (22/7) × 21 = 66 m
Therefore, length of rope required = circumference × 2 = 66 m × 2 = 132 m
Cost of rope = Rate × length
= 4 × 132 = Rs. 528
length of wire = circumference = πD
= 21π metres or appr 66 m
cost = 4(21π) = 84π
= 263.89 or appr Rs 264
To find the length of the wire the gardener needs to purchase, we need to calculate the circumference of the circular garden.
The formula to calculate the circumference of a circle is:
Circumference = π * diameter
In this case, the diameter of the circular garden is given as 21m, so we can substitute this value into the formula:
Circumference = π * 21
To find the length of the wire needed, we need to calculate the value of π (pi). Pi is a mathematical constant that is approximately equal to 3.14.
Circumference = 3.14 * 21
Calculating this gives us:
Circumference ≈ 65.94 meters
Therefore, the gardener needs to purchase a length of wire approximately equal to 65.94 meters.
To calculate the cost of the wire, we multiply the length of wire needed by the cost per meter:
Cost of wire = length of wire * cost per meter
= 65.94 meters * Rs.4 per meter
Calculating this gives us:
Cost of wire = 263.76 Rupees
Therefore, the cost of the wire at a rate of Rs.4 per meter is approximately 263.76 Rupees.