Question

Q. 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

Answer:

3.15 cm

Step-by-step explanation:

we have an equilateral triangle made up of wire whose one side is 6.6 cm

we know in equilateral triangle sides are equal

so total length of the wire will be

6.6 × 3 = 19.8

now that wire is drawn into circle.

The point to be focused on is that the length of the wire and circumference of the circle is same.

so

$19.8 = 2\pi \: r \\ 9.9 \div \pi = r$

r = 3.15cm

Answer 2

★Given :

• A piece of wire is bent into an equilateral triangle.

• Side of the equilateral triangle = 6.6 cm

• The wire is rebent into a circle.

★To Find :

• The radius of the circle.

★Solution :

Here a piece of wire is bent into an equilateral triangle and then into a circle.So first, we need to find the length of the wire by finding the perimeter of the given equilateral triangle.

We know :

✦Perimeter of Equilateral Triangle = 3 × Side

Where,

• Side = 6.6cm

Therefore,

→Perimeter  = 3 × 6.6

                   =19.8 cm

∴ The length of the wire is 19.8 cm

Now, as the wire of same length is bent into equilateral triangle and then into a circle,

→Perimeter of Equilateral Triangle = Perimeter of Circle

We know :

✦Circumference of Circle = 2πr

We have cirumference of the circle = 19.8cm.

Therefore,

→2πr = 19.8

→2(22/7)r = 19.8

→44/7 = 19.8 r

→r = 44/7 × 1/19.8

→r  = 19.8 × 7/44

→r = 138.6/44

→r = 3.15cm

Hence,the radius of circle is 3.15cm.

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