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.​

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 –

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

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

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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=21m
• cost of 1 metre rope=Rs.4.50
• No. Of round=2

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To find:-

• Length of rope for 2 times of fence
• Cost of rope needed

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Solution:-

To find the length of rope needed to fence 2 times, we have to find 2 times of the circumference of circle.

→ Given length of Diameter=21m

→ Radius will be D/2=(21m)/2

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~Finding circumference ::

$\large\underline{\boxed{\sf Circumference\:of\: circle=2\pi r}}\bigstar$

Now substituting the values:

$\sf Circumference\;of\: circle=2\times\dfrac{22}{7}\times\dfrac{21m}{2}$

$\sf Circumference\;of\: circle=\not 2\times\dfrac{22}{\not 7}\times\dfrac{\not 21m}{\not 2}$

$\sf Circumference\;of\: circle=22\times 3metre$

$\sf Circumference\;of\: circle=66metre$

Now 2 times of circumference will be 2×66m=132m

So the required length of rope is 132 metre.

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~Now find the cost of rope ::

Cost of 1 metre rope=Rs.4.5

Cost of 132 metre=Rs.132×4.5

Cost of 132 metre=Rs.594

So the required cost of rope is Rs.594.

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More to know!

${\leadsto\sf Area\; of \;circle=\pi r^2}$

${\leadsto{\textsf{Area of rectangle=Length \times \sf Breadth }}}$

${\leadsto{\textsf{Perimeter of rectangle=2(L+B)}}}$

${\leadsto\sf{Area\; of \:square=Side^2}}$

${\leadsto{\textsf{Perimeter of square =4\times Side}}}$

${\leadstosf{Area\: of \:triangle=\dfrac{1}{2} \times Base\times Height}}$

${\leadsto\textsf{Area of trapezium= \dfrac{1}{2}\times (sum of || Sides) \times Height}}$

${\leadsto\textsf{Area of quadrant= \dfrac{\pi r^2}{4} }}$

${\leadsto\textsf{Area of || gm =\sf D_1\times\sf D_2 }}$

${\leadsto\textsf{Radius= \dfrac{\sf Diameter}{2} }}$

${\leadsto\textsf{Volume of cube =Side^3 }}$

${\leadsto\textsf{Volume of cuboid=LBH}}$

${\leadsto\textsf{Volume of cylinder= \pi r^2h }}$

${\leadsto\textsf{Volume of cone= \dfrac{1}{3} \pi r^2h }}$

${\leadsto\textsf{Volume of sphere= \dfrac{4}{3}\pi r^3 }}$

${\leadsto\textsf{Volume of hemisphere= \dfrac{2}{3}\pi r^3 }}$

${\leadsto\textsf{Curved surface area of cylinder=2 \pi rh }}$