Question

A gardener wants to fence a circular garden of diameter 42 m. Find the length of the rope

he needs to purchase, if he makes 3 rounds of fence. Also find the cost of the rope, if it costs Rs.

4 per meter. (Take re =

22/7 )

Pls send it urgently

Answer 1

Given :

• A diameter of a circular garden =42m

• The cost of one rope = 4 per metre.

To Find :

•The length of the rope =?

Formula :

$\bullet \sf \: length = 2 \times circumference$

$\\ \bullet \sf \: radius = \frac{diameter}{2}$

$\bullet \sf \:circumference \: of \: the \: circle = 2\pi \: r$

Solution :

Since, the garden makes two rounds of the fence .

Thus,

Length of the rope required = 2 x circumference of circular garden.

$\\ \implies \sf \: radius = \frac{diameter}{2}$

$\\ \implies \sf \: radius = \frac{21}{2} m$

$\implies \boxed{ \sf{radius = \frac{21}{2} }}$

• Circumference of circular garden =$\sf{2 \pi r}$

$\implies \sf \: circumference = 2\pi \: r$

$\\ \implies \sf \: circumference = 2 \times \frac{22}{7} \times \frac{21}{2}$

$\\ \implies \sf \: circumference = 22 \times 3$

$\implies \boxed{\sf \: circumference = 66m}$

•Now, Length of rope required =2 x circumference of circular garden.

$\implies \sf \: length = 2 \times 66$

$\implies \boxed{ \bf\: length = 132m}$

Now, we also need to find cost of rope,

Given,

$\implies \sf \: cost \: of \: 1m \: rope = \: Rs. \: 4$

$\\ \implies \sf \: cost \: of \: 132m \: rope \: = Rs. \: 4 \times 132$

$\\ \implies \boxed{ \bf{cost \: of \: 132m \: rope = Rs. \: 528}}$

Therefore, It would cost Rs. 528 to fence the garden.

Answer 2

Answer:

$\fbox \pink{diameter} = 21m \\ \\ \fbox \purple{radius} = \frac{21}{2}m \\ \\ \fbox \red{circumference} = 2\pi \: r \\ \\ 2 \times \frac{22}{7} \times \frac{21}{2} = \frac{22}{7} \times 21 \\ \\ 22 \times 3 = 66m \\ \\ \fbox \green{length \: of \: rope \: required} = 2 \times 66 = 132m \\ \\ \fbox \blue{cost} = 1m \: rope = 4 \\ \\ 132m \: rope = 4 \times 132 = 528$