Area of a circle

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TACHS Math › Area of a circle

Questions 1 - 4

1

Find the area of a circle with the following radius:

$49\pi$

$14\pi$

$16\pi$

$7\pi$

$48\pi$

Explanation

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

$A=\pi r^2$

In this formula the radius is denoted by the variable, .

Substitute in the known variables and solve for the circle's area.

$A=\pi \times 7^2$

$A=49\pi$

2

Which is equal to the radius of a circle with area $400 \pi$

Explanation

The formula for the area of a circle, given its radius , is $A = \pi r^{2}$ . Replace with $400 \pi$ :

$\pi r^{2} = 400 \pi$

To find the radius , first, divide both sides by $\pi$ :

$\frac{\pi r^{2}}{\pi} = \frac{400 \pi}{\pi}$

$r^{2} = 400$

Now, find the square root of both sides. Since $400 = 20 \times 20$ , 20 is the square root of 400, so

.

The radius of the given circle is 20.

3

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

Explanation

Recall how to find the area of a circle:

$\text{Area of Circle}=\pi \times \text{radius}^2$

To find the length of the radius, divide the diameter by two.

$\text{radius}=\frac{12}{2}=6$

Now, plug it into the equation for the area of a circle.

$\text{Area of Circle}=\pi \times 6^2=36\pi=113.1$

4

To determine whether a machine on an assembly line is filling bottles with the correct amount of soda, twenty bottles are selected. The tenth bottle and every tenth bottle after that are taken off the line and examined.

This is an example of which kind of sampling?

Systematic sampling

Stratified sampling

Cluster sampling

Convenience sampling

Explanation

The sample in this scenario is selected from the population by choosing obects that occur at regular intervals. That makes this an example of systematic sampling.

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