A piece of wire is bent in shape of an equilateral triangle of each side $6.6\ cm$. It is rebent to form circular ring. What is the diameter of ring?

Given: A piece of wire is bent in shape of an equilateral triangle of each side $6.6\ cm$. It is rebent to form circular ring.

To do: To find the diameter of ring.

Solution:

As given, side of the triangle$=6.6\ cm$

$\therefore$ Perimeter of the equilateral triangle$=6.6+6.6+6.6$

$=19.8\ cm$

Now, let's $r$ be the radius of the ring.

Then, circumference of the ring$=$perimeter of the equilateral triangle

$\Rightarrow 2\pi r=19.8$

$\Rightarrow 2\times\frac{22}{7}\times r=19.8$

$\Rightarrow r=\frac{19.8\times7}{2\times22}$

$\Rightarrow r=3.15\ cm$

$\therefore$ Diameter of the ring$=2\times r$

$=2\times3.15$

$=6.30\ cm$

Thus, the diameter of the ring is $6.30\ cm$.

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Updated on: 10-Oct-2022

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