Question

A piece of wire is bent in the shape of an equilateral triangle each side 6.6 cm . It is re-bent to form a circular ring . What is the diameter of the ring​

Answer 1

Given

• A piece of wire is bent in the shape of an equilateral triangle each side 6.6 cm
• It is re-bent to form a circular ring

_______________________________

To Find

• The diameter of the ring

_______________________________

Solution

We'll firstly find the perimeter of the equilateral triangle to find the total length of the triangle.

Equilateral triangle consists of all equal sides.

Perimeter of equilateral triangle ⇒ 3 × Side

Perimeter of equilateral triangle ⇒ 3 × 6.6

Perimeter of equilateral triangle ⇒ 19.8 m

∴ The perimeter of the equilateral triangle is 19.8 m

We know that,

Perimeter of equilateral triangle = Circumference of the Ring

So, let's find the diameter with the help of the perimeter of the equilateral triangle.

Circumference ⇒ 19.8

Formula for Circumference ⇒ πd

Let's solve your equation step-by-step.

$\dfrac{22}{7}\times d = 19.8$

Step 1: Multiply 7/22 to both sides of the equation.

⇒ $\dfrac{22}{7}d\times \dfrac{7}{22} = 19.8 \times \dfrac{7}{22}$

⇒ $d = \dfrac{138.6}{22}$

⇒ $d = 6.3$

∴ The diameter of the ring is 6.3 cm

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Answer 2

Given :

A piece of wire is bent in the shape of an equilateral triangle each side 6.6 cm . It is re-bent to form a circular ring.

To FinD :

The diameter of the ring.

Solution :

Analysis :

Here first we have to take out the perimeter of the equilateral triangle. Then with the help of that perimeter we can find the radius of the circle because it is said that the wire is bent in the form of circle. And then by using the value of the radius we can get our answer of diameter.

Required Formula :

Circumference of circle = 2πr

where,

• π = 22/7
• r = radius

Explanation :

Perimeter :

We know that measures of all sides of a triangle add up to its perimeter.

We also know that all sides in equilateral triangle have same size.

☯ According to the question,

a + b + c = Perimeter₍ₜᵣᵢₐₙ₉ₗₑ₎

where,

• a = 6.6 cm
• b = 6.6 cm
• c = 6.6 cm

⇒ Perimeter₍ₜᵣᵢₐₙ₉ₗₑ₎ = 6.6 + 6.6 + 6.6

⇒ Perimeter₍ₜᵣᵢₐₙ₉ₗₑ₎ = 19.8

∴ Perimeter of triangle = 19.8 cm.

It is said that the same wire is re-bent to form a circular ring.

☯ According to the question,

⇒ Perimeter₍ₜᵣᵢₐₙ₉ₗₑ₎ = Perimeter₍꜀ᵢᵣ꜀ₗₑ₎

⇒19.8 = 19.8

∴ Perimeter or circumference of circle = 19.8 cm.

Let the radius be "r" cm.

We know that if we are given the circumference of the circle and is asked to find the radius then our required formula is,

Circumference of circle = 2πr

where,

• π = 22/7
• r = r cm
• Circumference = 19.8 cm

Using the required formula and substituting the values,

⇒ Circumference of circle = 2πr

⇒ 19.8 = 2 × 22/7 × r

⇒ 19.8 = 44/7 × r

⇒ 19.8 × 7/44 = r

⇒ 138.6/44 = r

⇒ 3.15 = r

∴ Radius of circle = 19.8 cm.

Diameter = 2 × Radius

= 2 × 3.15

= 6.30

= 6.3 cm

Diameter of the ring is 6.3 cm.