Question

The gardener wants to fence a circular diameter of 21m. find the length of the rope he needs to purchase if he makes 2rounds of fence. also find the cost of rope if it is Rs.4 per meter.

Answer 1

Given:

• The gardener wants to fence a circular diameter of 21m.

To Find:

• Find the length of the rope he needs to purchase if he makes 2rounds of fence.
• Also find the cost of rope if it is Rs.4 per meter.

Solution:

• Diameter = 21 m
• Radius = 21/2 m

Circumference of garden = 2πr

➠ 2 × 22/7 × 21/2

➠ 22/7 × 21

➠ 22 × 3

➠ 66 cm

Length of rope required = 2 × Circumference of garden

➠ Length of rope = 2 × 66

➠ Length of rope = 132 m

Now, we have to find cost of rope

➠ Cost of 1m rope = Rs.4

➠ Cost of 132m rope = 132 × 4 = Rs. 528

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

Answer 2

$\underline{\underline{\sf{\maltese\:Given\::-}}}$

• circular diameter = 21m.

$\underline{\underline{\sf{\maltese\:To\:Find\::-}}}$

• Find the length of the rope he needs to purchase if he makes 2rounds of the fence.
• Find the cost of rope if it is Rs.4 per meter

$\underline{\underline{\sf{\maltese\:Concept\::-}}}$

$\odot$ Here we have given that the gardener wants to fence a circular diameter of 21m. As we know that to find the length of the rope we need the circumference of the garden, so firstly we will find out the circumference of the garden.

$\odot$ After finding the circumference of the garden we will find out the length of the rope if the gardener wants to makes 2rounds of the fence.

$\odot$ Now after finding the length of the rope we will find out the cost of rope if it is Rs.4 per meter.

$\underline{\underline{\sf{\maltese\:Full\:Solution\::-}}}$

$\bigstar$ Let us find out the circumference of the circular garden by using the formula ( Circumference of the circular garden = 2πr )

Diameter = 21m

Radius = diameter/2

Radius = 21/2m

$\qquad\tt{:\implies\:Circumference\:of\:the\:garden\:=\:2\:\pi r}$

$\qquad\tt{:\implies\:Circumference\:of\:the\:garden\:=\:2\:\times\:\dfrac{22}{7}\: \times\:\dfrac{21}{2}}$

$\qquad\tt{:\implies\:Circumference\:of\:the\:garden\:=\:\:\dfrac{22}{7}\: \times\:21}$

$\qquad\tt{:\implies\:Circumference\:of\:the\:garden\:=\:22\: \times\:3}$

$\qquad\tt{:\implies\:Circumference\:of\:the\:garden\:=\:66}$

Hence the circumference of the circular garden is 66m.

$\qquad\qquad\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}$

$\bigstar$ Let us find out the length of the rope by the product of 2 and the circumference of the garden.

$\qquad\tt{:\implies\:Length\:of\:the\:rope\:=\:2\:\times\:circumference\:of\:the\:garden}$

$\qquad\tt{:\implies\:Length\:of\:the\:rope\:=\:2\:\times\:66}$

$\qquad\tt{:\implies\:Length\:of\:the\:rope\:=\:132\:m}$

Hence the length of the rope if the gardener wants to makes 2rounds of the fence is 132 m.

$\qquad\qquad\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}$

$\bigstar$ Let us find out the cost of the rope if it is Rs.4 per meter.

$\qquad\tt{:\implies\:Cost\:of\:1\:m\:rope\:=\:Rs.\:4}$

$\qquad\tt{:\implies\:Cost\:of\:132\:m\:rope\:=\:132\:\times\:4}$

$\qquad\tt{:\implies\:Cost\:of\:132\:m\:rope\:=\:Rs.\:528}$

Hence the cost of the 132m rope is Rs. 528

$\qquad\qquad\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}$