Question

A gardener wants to fence a circular garden of diameter 21 m. Find the length of the rope he needs to purchase, if he makes 2 rounds of fence. Also, find the cost of the rope, if it costs Rs. 4 per meter. (Take $\pi = \dfrac{{22}}{7}$)

Answer 1

Hint:
In this question, we will find the circumference of the circular garden. So that we can find the length of the rope. But remember one thing there are 2 rounds of fence. So, we will do twice the circumference. Then we will find the cost of rope by multiplying it with the cost of per meter of rope that is Rs, 4 per meter.

Complete step by step solution:
Diameter of a circular garden = 21 m
Radius of a circular garden = $\dfrac{{Diameter}}{2} = \dfrac{{21}}{2}$m
To find the length of the rope he needs to purchase, if he makes 2 rounds of fence, we need to find the circumference of the circular garden.
Circumference of the circular garden = $2\pi r$= $2 \times \dfrac{{22}}{7} \times \dfrac{{21}}{2}$= 66 m
Circumference of the circular garden is 66 m then it means to fence the garden once the gardener needs 66 m of rope.
To fence the garden twice = 2 X circumference of a circular garden
 = 2 X 66 = 132 m
Length of the rope gardener needs to purchase for fencing two rounds = 132 m (Ans.)
Cost of one meter of rope = Rs. 4

Cost of 132 m of rope = 132 X 4 = Rs. 528 (Ans.)

Note:
You have to be careful that in the question diameter is given. So, we will find the radius. We know that radius = 2 X diameter. Then we will find the circumference of the circular garden by using this formula $2\pi r$. One more thing you need to remember that the value of pi is $\dfrac{{22}}{7}$ and 3.14. you can use any of the two values of pi unless it is not specified in the question. In this question we have already given the value of pi that is $\dfrac{{22}}{7}$.