Question

What is the circumference of a circle with a diameter of 8 inches?

a 12.56
b 25.12
c 50.24
d 200.96

Answer 1

Circle:

A Circle is a closed plane geometric shape figure. The diameter of a circle is the longest chord of a circle. The radius drawn perpendicular to the chord bisects the chord. A Circle is always lie at an equal distance from a center point. Circles having different radius are similar.

Circumference of Circle:

The circumference of a circle is the product of pi and length of the diameter of a circle. Mathematically;

`\longrightarrow \tt{Circumference_((circle)) = \pi{D}}`

Here, D is the diameter of the circle or distance between the circle.

Elucidation:

We are asked to find the circumference of the circle if the diameter is 8 inches.

We know that, The circumference of a circle is the product of pi and length of the diameter of a circle. Therefore;

`\implies \tt{Circumference_((circle)) = \pi{D}}`

`\implies \tt{Circumference_((circle)) = 3.14 * 8}`

`\implies \boxed{\pmb{\tt{Circumference_((circle)) = 25.12}}}`

Hence, the circumference of the circle is 25.12 inches. So option (B) is correct.

Answer 2

• Circumference of circle = 25.12 inches
• Thus Option B is correct .

Explanation:

In the question we are given that diameter of circle is of 8 inches . And we have asked to find the circumference of the circle .

For finding circumference of circle we must have to know that what is the formula for finding circumference of circle. So :

`\quad \quad \: \red{\underline{\pink{ \boxed{ \frak{Circumference \: of \: Circle =2 \pi r }}}}}`

Where ,

• π refers to 3.14

• r refers to radius of circle

Solution : -

As in the question we are given length of diameter . So for finding circumference we need to find the radius of circle .

We know that diameter of circle is two times its radius ,

`\qquad \: \rm {Diameter = 2 × Radius }`

So for radius we are dividing both side with 2 :

`\qquad \: \rm { (Diameter)/(2) = \frac{ \cancel{2} × Radius}{ \cancel{2}} }`

We get that ,

`\qquad \: \rm {Radius = (Diameter)/(2) }`

Therefore , we can say that radius of circle is half of its diameter .

Now using this , firstly we are finding radius of circle . So :

`\longmapsto \quad \: \boxed{\rm{ Radius = (8)/(2) \: \: inches}}`

• Therefore , radius of circle is 4 inches .

Now , we are moving towards our final solution .

So ,

`\longmapsto \quad Circumference_ { (Circle)} =2 * 3.14 * 4`

Multiplying 2 with 3.14 :

`\longrightarrow \quad Circumference_ { (Circle)} = 6.28 * 4`

Multiplying 4 and 6.28 :

`\longrightarrow \quad \purple{{\boxed{\frak{Circumference_ { (Circle)} = 25.12\: inches }}}}`

• Therefore , circumference of circle having diameter 8 inches is 25.12 inches and hence option b is correct .

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