Question

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

Answer 1

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.

$2\times \dfrac{22}{7} \times x = 19.8$

Step 1: Simplify the equation.

⇒ $2\times \dfrac{22}{7} \times x = 19.8$

⇒ $\dfrac{44}{7}x = 19.8$

Step 2: Multiply $\frac{7}{44}$ to both sides of the equation.

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

⇒ $x = \dfrac{138.6}{44}$

⇒ $x = 3.15$

∴ The radius of the circle is 3.15 cm

_________________________________

Answer 2

Answer:

Given :-

• A piece of wire is bend into an equilateral triangle of side 6.6 cm the wire is bent into a circle.

To Find :-

• What is the radius of the circle.

Formula Used :-

${\red{\boxed{\large{\bold{Circumference\: of\: circle =\: 2{\pi}r}}}}}$

where,

• r = Radius

Solution :

First, we have to find the length of the wire,

Given :

• Side = 6.6 cm

Then,

↦ Length = 3 × 6.6

➦ Length = 19.8 cm

Hence, the length of the wire is 19.8 cm.

Now, we have to find the radius,

Given :

• Length = 19.8 cm

According to the question by using the formula we get,

⇒ $\sf 2 \times \dfrac{22}{7} \times r =\: 19.8$

⇒ $\sf r =\: \dfrac{19.8 \times 7}{2 \times 22}$

⇒ $\sf r =\: \dfrac{138.6}{44}$

⇒ $\sf r =\: \dfrac{1386}{44 \times 10}$

⇒ $\sf r =\: \dfrac{1386}{440}$

➠ $\sf\bold{\purple{r =\: 3.15\: cm}}$

$\therefore$ The radius of the circle is 3.15 cm .