Question

A wire in the shape of a square, with each
side equal to 15.5 cm, is bent into the
shape of a circle. Find the circumference
and the diameter of the circle.​

Answer 1

Given :-

• Wire is in shape of square with side 15.5cm
• It is then bent in shape of circle.

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To find :-

• The circumference of circle
• Diameter of circle.

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Formulae to remember :-

• Perimeter of square : 4 × side.
• Circumference of circle = πd

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Understanding the question :-

• In this question we are given that a wire is in the shape of square with side 15.5cm and then we bent into the shape of circle this means that perimeter of square = circumference of circle. And then finding the diameter from the circumference of circle.

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So, Let's Solve it :-

Finding the perimeter of square :

➱ Perimeter of square = 4 × side

➨ 4 × 15.5

➨ 62 cm

Now,

As we know that Perimeter of square = Circumference of circle.

Therefore :

➱ Circumference of circle = 62 cm

Finding the diameter :-

➱ Circumference of circle = πd

➨ 62 = 22 /7 × d

➨ ( 62 × 7 )/ 22 = d

➨ 19.72 = D

➱ Diameter of circle = 19.72 cm .

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Therefore :

• Circumference of circle = 62 cm
• Diameter of circle = 19.72 cm

Answer 2

Given: A wire of square shape, Side of the square is 15.5cm, It is bent into circle.

Need to find: Circumference and diameter?

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❍ Let's consider radius of circle be r.

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As we know that,

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$\begin{gathered}\star\:{\underline{\boxed{\frak{Perimeter_{\:(Square)} = 4 \times side}}}}\\\\\\ \bf{\dag}\:{\underline{\frak{Putting\:given\:values\:in\:formula,}}}\\\\\\ :\implies\sf 4 \times 15.5 \\\\\\ \implies{\underline{\boxed{\frak{\purple{62 \: cm}}}}} \\\\\\ :\implies\sf 2\pi r = 62cm\\\\\\ :\implies\sf 2 \times \frac{22}{7} \times r = 62\\\\\\ :\implies\sf 2 \times \frac{11}{7} \times r=31 \\\\\\ :\implies\sf 3.14 \times r = 31 \\\\\\ :\implies\sf r = \frac{31 }{3.14} \\ \\ \\ \implies{\underline{\boxed{\frak{\purple{r = 9.87}}}}}\:\bigstar\\\\\end{gathered}$

• Here, Perimeter of the square = Circumference of the circle.

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Therefore,

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Circumference of the circle, 62 cm

Diameter of the circle, r × 2 = 9.87 × 2 = 19.74 cm

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$\therefore\:{\underline{\sf{Hence,\: Circumference \: and \: diameter\:are\:\bf{62\:cm}\: \sf{and}\: \bf{19.74\:cm}\: \sf{respectively}.}}}$