Pre-Algebra - Area of a Circle

If a circular island has a diameter of 12 miles, what is the area of the island?

$36\pi$

$16\pi$

$2\pi$

$12\pi$

Explanation

The formula for the area of a circle is $\pi r ^{2}$ ("" is for radius). However, the question only gives us the diameter, so we must determine the radius ourselves first.

A radius is half a diameter, therefore if the diameter is 12 miles then the radius is 6 miles.

Now we can plug in 6 for "" and solve.
$\pi (6^{2}) =$
$36\pi$

Solve for the area of a circle if the radius is .

$4\pi x^2$

$4\pi x$

$4\pi^2 x^2$

$4\pi + \pi x^2$

Explanation

Write the formula to find the area of a circle.

$A=\pi r^2$

Substitute the radius.

$A=\pi (2x)^2 = 4\pi x^2$

What is the area of a circle with a diameter of , rounded to the nearest whole number?

$\dpi{100} 64$

$\dpi{100} 254$

$\dpi{100} 255$

$\dpi{100} 81$

Explanation

The formula for the area of a circle is

$\dpi{100} \pi r^{2}$

Find the radius by dividing 9 by 2:

$\dpi{100} \frac{9}{2}=4.5$

So the formula for area would now be:

$\dpi{100} \pi r^{2}=\pi (4.5)^{2}=20.25\pi \approx 63.6= 64$

What is the area of a circle with a diameter equal to 6?

$9\pi$

$3\pi$

$18\pi$

$36\pi$

Explanation

First, solve for radius:

$r=\frac{d}{2}=\frac{6}{2}=3$

Then, solve for area:

$A=r^2\pi=3^2\pi=9\pi$

The diameter of a circle is . Give the area of the circle in terms of .

Explanation

The area of a circle can be calculated using the formula:

$Area=\frac{\pi d^2}{4}$ ,

where is the diameter of the circle and $\pi$ is approximately .

$Area=\frac{\pi (4t)^2}{4}=\frac{16\pi t^2}{4}=4\pi t^2 \Rightarrow Area\approx 4\times 3.14\times t^2$

$\Rightarrow Area\approx 12.56t^2$

What is the area of a circle that has a diameter of inches?

Explanation

The formula for finding the area of a circle is $\pi r^{2}$ . In this formula, represents the radius of the circle. Since the question only gives us the measurement of the diameter of the circle, we must calculate the radius. In order to do this, we divide the diameter by .

$\frac{15}{2}=7.5$

Now we use for in our equation.

$\pi (7.5)^{2}=176.7146 : in^{2}$

Units = cm

Diameter is 12, find the area of the circle.

$\small 113.04cm^{2}$

$\small 13cm^{2}$

$\small 100.04cm^{2}$

$\small 129.04cm^{2}$

Explanation

To find the area of a circle we use the equation:

$A=\small \pi(r)^{2}$ .

In this question we are told that the diameter of the circle, meaning the radius is half of this.

To solve for the area, we just plug it into our equation:

$r=\frac{1}{2}d\rightarrow r=\frac{1}{2}12=6$

$\A=\small \small \small \small \small \small \small \small \pi(6)^{2} \A= 6\times6\times \pi \A= 36\pi \A= 36\times 3.14\A=113.04cm$ .

And because we are working with the area of a shape, our answer must have units that are squared, therefore: $\small \small \small \small \small \small 113.04cm^{2}$ .