Calculating Wire Length from Circle
The problem states a wire is bent into a circle with a radius ($r$) of $70 \text{ cm}$. The length of the wire is equal to the circumference of this circle.
The formula for the circumference ($C$) of a circle is $C = 2 \pi r$. Using the given value $\pi = \frac{22}{7}$ and $r = 70 \text{ cm}$: $C = 2 \times \frac{22}{7} \times 70 \text{ cm}$ $C = 2 \times 22 \times 10 \text{ cm}$ $C = 440 \text{ cm}$
So, the total length of the wire is $440 \text{ cm}$.
Finding Square Side Length
The same piece of wire, with length $440 \text{ cm}$, is then bent to form a square. The length of the wire now represents the perimeter ($P$) of the square.
The formula for the perimeter ($P$) of a square with side length $s$ is $P = 4s$. Since the wire's length is $440 \text{ cm}$, we have: $4s = 440 \text{ cm}$
To find the side length ($s$), divide the perimeter by 4: $s = \frac{440 \text{ cm}}{4}$ $s = 110 \text{ cm}$
Therefore, the length of the side of the square will be 110 cm.
Similar Questions
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Important Questions from 2-D Mensuration
- The sides of a rectangular field are 169 m and 154 m long. Its area is equal to the area of a circular field. What is the circumference (in m) of the circular field? Take $\pi = \frac{22}{7}$
- Find the area of a sector with a central angle of 150° in a circle with a radius of 12 cm.
- The area of a square is $2304$ cm$^2$. Its perimeter is equal to the perimeter of a regular hexagon. What is the area (in cm$^2$) of the hexagon?
Calculate the area of the triangle whose sides are 8 cm, 9 cm and 13 cm. (Rounded up to two decimal places)
- The length of a rectangular pitch is 30 m more than its breadth. Its area is $18,271$ m$^{2}$. Its breadth (in m) is:
