Ex.11.3 Q4 Perimeter and Area - NCERT Maths Class 7

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Question

A gardener wants to fence a circular garden of diameter \(21\rm\,m.\) 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 \(\rm{Rs}\,4\) per meter.

\(\begin{align}\left( {{\rm{Take }}\pi = \frac{{22}}{7}} \right)\end{align}\)

Text Solution

What is known?

Diameter of circular garden and the cost of one meter of rope.

What is unknown?

The length of the rope required if the gardener wants to make \(2\) rounds of fence and also the cost of the rope, if it costs ₹ \(4\) per meter.

Reasoning:

As the diameter is given as \(21 \rm\,m\) that means the radius will be the half of the diameter. Using the diameter, circumference of the circular garden can be calculated. Since the gardener wants to make \(2\) rounds of fence, the length of rope required will be two time the circumference. The cost of the rope can be obtained by multiplying length of the rope with cost of one meter of the rope.

Steps:

Diameter of the circular garden

\(= 21 \rm\,m\)

Radius of the circular garden

\(\begin{align}=\frac{{21}}{2}\,\rm{m}\end{align}\)

Now,

Circumference of circular garden

\[\begin{align}&= 2\pi r\\ &= 2 \times \frac{{22}}{7} \times \frac{{21}}{2}\\&= 66\;\rm{m}\end{align}\]

Since, the gardener wants to make \(2\) rounds of fence, so the total length of the rope required for fencing \(= 2 \,\times \, 66 = 132\rm\, m\)

Since, the cost of \(1\)-meter rope \(= ₹ \,4\)

Therefore, the cost of \(132\)-meter rope \(= 4 \times 132 = ₹\, 528\)