Question

A gardener want to fence a circular garden of diameter 21m. Find the length of rope he needs to purchase,if he makes 2 rounds of fence. Also find the cost of rope, if it's price is rs. 4.50 per meter.
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Answer 1

Given :-  

• A gardener want to fence a circular garden of diameter 21 m
• He makes 2 rounds of fence with rope
• Cost of rope is Rs. 4.50 per meter

To Find :-  

• Length required to make 2 rounds of fence and cost if it’s price is Rs. 4.50 per m  

Solution :-  

~Here, we’re given the diameter of circular garden and we need to find the length of rope needed to make two rounds and cost of rope. For length of rope we need to find the circumference of the circular garden and then the cost.  

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Finding the radius –  

$\large\underline{\boxed{\bf\pink{\star\;\; Radius= \dfrac{Diameter}{2}}}}$  

$\sf \implies \dfrac{21}{2} \; m$

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Finding the circumference –  

$\large\underline{\boxed{\bf\pink{\star\;\;Circumference = 2 \pi r}}}$

$\sf \implies 2 \times \dfrac{21}{2} \times \dfrac{22}{7}$

$\sf \implies 3 \times 22$

$\sf \implies 66\;m$

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→ As , we need to find the rope if he takes 2 rounds so we will multiply the circumference with 2  

$\sf \implies 66 \times 2$

 

$\sf \implies 132\;m$

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Finding the cost :-  

$\sf \implies 1\;m = Rs. \; 4.50$

 

$\sf \implies 132\;m = 132 \times 4.50$

 

$\sf \leadsto Rs.\;594$

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Therefore ,  

The rope required is 132 m and cost is Rs. 594  

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Answer 2

Given :-

• Diameter of Circular Garden = 21m
• He makes 2 rounds of fence with rope
• Cost of rope is Rs. 4.50 per m

To Find :-

• Length of Rope required to make 2 rounds of fence and cost of rope.

Solution :-

❏ As we know that, fencing is done on the boundary , so we have to find the Circumference of the Circle .

⟾ Circumference of Garden = πd

⟾ Circumference of Garden = 22/7 × 21

⟾ Circumference of Garden = 22 × 3

⟾ Circumference of Garden = 66m

So, 66m of rope is required to fence the Garden in 1 time.

Now,

⟾ Rope required in 2 rounds = 66 × 2

⟾ Rope required in 2 rounds = 132m

Therefore, 132m of rope is required to fence the Garden 2 times.

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➞ Cost of 1m rope = 4.50

➞ Cost of 132m rope = 4.50 × 132

➞ Cost of 132m rope = Rs 594

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Therefore :

• Total Rope required = 132m
• Cost of Total Rope = Rs 594

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