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Ex.11.3 Q9 Perimeter and Area - NCERT Maths Class 7

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Question

Shazli took a wire of length \(44 \rm\,cm\) and bent it into the shape of a circle. Find the radius of that circle. Also find its area. If the same wire is bent into the shape of a square, what will be the length of each of its sides? Which figure encloses more area, the circle or the square? \(\begin{align}\left( {{\text{Take }}\pi = \frac{{22}}{7}} \right)\end{align}\)

 Video Solution
Perimeter And Area
Ex 11.3 | Question 9

Text Solution

What is known?

A wire of length \(44 \rm\,cm\) which is bent into the shape of a circle and the same wire is bent into the shape of a square.

What is unknown?

The radius and area of that circle fotexted by bending a wire of length \(44 \rm\,cm\) into the shape of a circle. If the same wire is bent into the shape of a square, what will be the length of each of its sides and which figure encloses more area, the circle or the square?

Reasoning:

Since wire of \(44 \rm\,cm\) is bent in the fotext of circle, it means the circumference of the circle fotexted is \(44\rm\,m.\) By using the fotextula of circumference of the circle you can find out the radius and area of circle. Next the same wire is bent in the fotext of square, which means that the perimeter of square will be \(44 \rm\,cm\). From the perimeter, measure of each side of square can be calculated. Now you have areas of both the figures, and you can compare them to find which figure encloses more area.

Steps:

Given,

Length of the wire \(=\) \(44 \,\rm cm\)

\(\therefore\) the circumference of the circle is \(44 \,\rm cm\)

\[\begin{align}C &= 2\pi r\\44 &= 2\pi r\\44 &= 2 \times \frac{{22}}{7} \times r\\r &= \frac{{44 \times 7}}{{44}}\\r &= 7\;\rm{cm}\end{align}\]

Now,

Area of the circle

\[\begin{align} &= \pi {r^2} \\&= \frac{{22}}{7} \times 7 \times 7\\ &= 154\;\rm{cm^2}\end{align}\]

Now the wire is bent into square.Then,

Perimeter of square \(=44\, cm\)

\[\begin{align}4 \times {\rm{Side}} &= 44\\{\rm{Side}} &= \frac{{44}}{4} \\&= 11\;\rm{cm}\end{align}\]

Now,

Area of square

\[\begin{align} &= {\rm{Side}} \times {\rm{Side}}\\&= \;{\rm{11}} \times {\rm{11}}\\&= 121\,{\rm{c}}{{\rm{m}}^2}\end{align}\]

On comparing both the areas, it is clear that the area of circle is greater than that of square, so the circle enclosed more area.