Question

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A piece of wire is bent into an equilateral triangle of side 6.6 cm the wire is then bent into a circle.What is the radius of the circle?


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Answer 1

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Given

A piece of wire is bent into an equilateral triangle.

Side of the equilateral triangle is 6.6 cm

The wire is rebent into a circle.

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To Find

The radius of the circle.

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Solution

First, we'll find the length of the wire. To do that we'll find the perimeter of the given equilateral triangle.

Perimeter of Equilateral Triangle ⇒ 3 × Side

Side ⇒ 6.6

Perimeter of the Given Equilateral Triangle ⇒ 3 × 6.6

Perimeter of the Given Equilateral Triangle ⇒ 19.8 cm

∴ The length of the wire is 19.8 cm

Perimeter of Equilateral Triangle = Perimeter of Circle

Perimeter of Circle ⇒ 2πr

Perimeter of Given Circle ⇒ 19.8 cm

Let's solve the following equation to find the radius of the circle step-by-step.

2\times \dfrac{22}{7} \times x = 19.82× 722

×x=19.8

Step 1: Simplify the equation.

⇒ 2\times \dfrac{22}{7} \times x = 19.82× 722 ×x=19.8

⇒ \dfrac{44}{7}x = 19.8 744

x=19.8

Step 2: Multiply \frac{7}{44}

44

7

to both sides of the equation.

⇒ \dfrac{7}{44} \times \dfrac{44}{7}x = 19.8\times \dfrac{7}{44}

447 × 744

x=19.8× 447

⇒ x = $\dfrac{138.6}{44}$

⇒ x = 3.15x=3.15

∴ The radius of the circle is 3.15 cm

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Answer 2

Given

A piece of wire is bent into an equilateral triangle.

Side of the equilateral triangle is 6.6 cm

The wire is rebent into a circle.

_________________________________

To Find

The radius of the circle.

_________________________________

Solution

First, we'll find the length of the wire. To do that we'll find the perimeter of the given equilateral triangle.

Perimeter of Equilateral Triangle ⇒ 3 × Side

Side ⇒ 6.6

Perimeter of the Given Equilateral Triangle ⇒ 3 × 6.6

Perimeter of the Given Equilateral Triangle ⇒ 19.8 cm

∴ The length of the wire is 19.8 cm

Perimeter of Equilateral Triangle = Perimeter of Circle

Perimeter of Circle ⇒ 2πr

Perimeter of Given Circle ⇒ 19.8 cm

Let's solve the following equation to find the radius of the circle step-by-step.

2\times \dfrac{22}{7} \times x = 19.82× 722

×x=19.8

Step 1: Simplify the equation.

⇒ 2\times \dfrac{22}{7} \times x = 19.82× 722 ×x=19.8

⇒ \dfrac{44}{7}x = 19.8 744

x=19.8

Step 2: Multiply \frac{7}{44}

44

7

to both sides of the equation.

⇒ \dfrac{7}{44} \times \dfrac{44}{7}x = 19.8\times \dfrac{7}{44}

447 × 744

x=19.8× 447

⇒ x = \dfrac{138.6}{44}

44

138.6

⇒ x = 3.15x=3.15

∴ The radius of the circle is 3.15 cm

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