Question

The diameter of a circle is 3 miles. What is the area?

Answer 1

The answer is:

A = 7.069 miles²

Work/explanation:

We have the diameter, but we need to find the radius. We can do that by diving the diameter by 2:

radius = diameter ÷ 2 = 3 ÷ 2 = 1.5 miles

Now we move on to the next step - the formula.

The formula is:

`\sf{A=\pi r^2}`

where:

• A = area
• π = pi
• r = radius

diagram

`\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\small 1.5\ miles}\end{picture}`

Plug in the data

`\sf{A=\pi * 1.5^2}`

`\sf{A=\pi*2.25}`

`\sf{A=7.069~miles^2}`

Hence, this is the area

Answer 2

Area = 7.065 square miles

Explanation:

The diameter of a circle is the distance across the circle passing through its centre, and it is equal to twice the radius. Therefore, if the diameter of a circle is 3 miles, then the radius is 1.5 miles.

The formula for the area of a circle is
`A = \pi r^2` (
`A = \pi * r^(2)`)

• 
  `A` is the area
• 
  `r` is the radius.
• The value of pi (
  `\pi`) is approximately 3.14, so we will use that value.

Substituting the value of the radius into this formula, we get:

• 
  `A = 3.14 * 1.5^2`
• 
  `A = 3.14 * 2.25`
• 
  `A = 7.065`

Therefore, the area of the circle is approximately 7.065 square miles.

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