7th Grade Math - Area of a circle

The radius of a circle is 4 cm, what is the area?

$50.2\ cm^{2}$

$12.6\ cm^{2}$

$78\ cm^{2}$

$28.3\ cm^{2}$

$58.7\ cm^{2}$

Explanation

The area of a circle is found by: $Area=r^{2}\pi$ , where r is the radius.

$4^{2} \pi = 50.2$ .

The area of the circle is $50.2\ cm^{2}$ .

The radius of a circle is $\frac{2}{\sqrt{\pi }}$ . Give the area of the circle.

$4\pi$

$\frac{4}{\pi }$

$2\pi$

Explanation

The area of a circle can be calculated as $Area=\pi r^2$ , where is the radius of the circle, and $\pi$ is approximately .

$Area=\pi r^2=\pi\times (\frac{2}{\sqrt{\pi}})^2=\pi\times \frac{4}{\pi}\Rightarrow Area=4$

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:

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

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 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:

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

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 .