Question

the piece of wire is bent in the shape of an equilateral triangle of side 7.2 cm It is bent to form a circular ring . find the diameter of the ring?​

Answer 1

Question:

The piece of wire is bent in the shape of an equilateral triangle of side 7.2 cm. It is bent to form a circular ring . Find the diameter of the ring?​

Answer:

The diameter of the ring is 6.88 cm.

Given:

The piece of wire is bent in the shape of an equilateral triangle of side 7.2 cm.

It is bent to form a circular ring .

To find:

The diameter of the ring.

Explanation:

The piece of wire is bent in the shape of an equilateral triangle of side 7.2 cm.

∴ Perimeter of the triangle=( 3×side)

                                         =(3×7.2) cm

                                         = 21.6 cm.

The perimeter of the triangle = The circumference of the circle = 21.6 cm.

We know that,

Circumference = 2πr

∴ 21.6  = 2πr

⇒2πr = 21.6

⇒πr = (21.6÷2)

⇒ πr = 10.8

⇒ r = 10.8÷(22/7) [∵ Putting the value of π.]

⇒ r = (10.8×7/22)

⇒ r = 3.436

⇒ r = 3.44 cm

The radius of the circle is 3.44 cm.

As we know that,

Radius is 1/2 of the diameter.

∴ The diameter of the circle is =(3.44×2) cm

                                                = 6.88 cm.

∴ The diameter of the circle is 6.88 cm.

Answer 2

Given: A wire bent in the shape of an equilateral triangle of side 7.2 cm. It is further bent to form a circular ring.

To find: The diameter of the circular ring.

Answer:

Let's first find the perimeter of the triangle.

Formula to do so [for equilateral triangles]: 3 * side.

It's given that the length of a side of the triangle is 7.2. Therefore, its perimeter would be:

3 * 7.2 = 21.6 cm

Now, as per the question, perimeter of the triangle = circumference of the circle.

Therefore, we can say that the circumference of the circle is 21.6 cm as well.

Formula to find the circumference of a circle: 2 * π * r.

Equating 21.6 to the formula,

$\sf 21.6\ =\ 2\ \times\ \dfrac{22}{7}\ \times\ r\\\\\\21.6\ =\ \dfrac{44}{7}\ \times\ r\\\\\\151.2\ =\ 44\ \times\ r\\\\\\3.43\ cm\ =\ r$

We now have the radius [r]. We can find the diameter.

Diameter = 2 * r = 2 * 3.43 = 6.86 cm.

Therefore, the diamter of the ring is 6.86 cm.