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Find the area of a circle with a circumference of 6.28 units.
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Answer 1

Approximately 3.14

The formula for circumference of a circle with radius
`r` is
`2\pi r`.

The formula for the area of a circle with radius
`r` is
`\pi r^2`.

`\pi \thickapprox3.14`

So the radius of our circle is
`(6.28)/(2\pi ) \thickapprox(6.28)/(2*3.14) =1`

and its area is
`\pi r^2\thickapprox3.14*1^2=3.14`

The number
`\pi` is defined as the ratio of the circumference of a circle to its diameter (i.e. to twice its radius), hence the formula
`2\pi r`

To see that the area of a circle is
`\pi r^2` you can divide it into a number of equal segments and stack them head to tail to form a sort of parallelogram with 'bumpy' sides. the long sides will be about half the circumference in length - that is
`\pi r`, while the height of the parallelogram will be about
`r`. So the area is seen to be about
`\pi r^2`.

Answer 2

Area of circle is 3.14 units.

step-by-step Step-by-step explanation:

Given:

• ➛ Circumference = 6.28 units

To Find:

• ➛ Radius of circle
• ➛ Area of circle

Using Formulas :

• ➛ Circumference of circle = 2πr
• ➛ Area of circle = πr²

Where

• ➛ π = 3.14
• ➛ r = radius

Solution :

Firstly finding the radius of circle,

`\sf{\implies{Circumference_((Circle)) = 2 \pi r}}`

`\sf{\implies{6.28= 2 * 3.14 * r}}`

`\sf{\implies{6.28= 6.28 * r}}`

`\sf{\implies{r = (6.28)/(6.28)}}`

`\sf{\implies{r = \cancel{(6.28)/(6.28)}}}`

`\sf{\implies{r = 1 \: unit}}`

Hence, the radius of circle is 1 unit.

`\begin{gathered} \end{gathered}`

Now, calculating the area of circle

`\sf{\longrightarrow{Area_((Circle)) = \pi{r}^(2)}}`

`\sf{\longrightarrow{Area_((Circle)) = 3.14 * {(1)}^(2)}}`

`\sf{\longrightarrow{Area_((Circle)) = 3.14 * 1}}`

`\sf{\longrightarrow{Area_((Circle)) = 3.14 \: unit}}`

Hence, the area of circle is 3.14 units.

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