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TACHS Math : Area of a circle

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Example Questions

Example Question #1 : Area

Find the area of a circle with the following radius:

r=7 $\displaystyle r=7$

Possible Answers:

$49\pi$ $\displaystyle 49\pi$

$14\pi$ $\displaystyle 14\pi$

$48\pi$ $\displaystyle 48\pi$

$7\pi$ $\displaystyle 7\pi$

$16\pi$ $\displaystyle 16\pi$

Correct answer:

$49\pi$ $\displaystyle 49\pi$

Explanation:

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

$A=\pi r^2$ $\displaystyle A=\pi r^2$

In this formula the radius is denoted by the variable, $\displaystyle r$.

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

$A=\pi \times 7^2$ $\displaystyle A=\pi \times 7^2$

$A=49\pi$ $\displaystyle A=49\pi$

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Example Question #3 : Area

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

Possible Answers:

$\displaystyle 20$

100 $\displaystyle 100$

$\displaystyle 40$

200 $\displaystyle 200$

Correct answer:

$\displaystyle 20$

Explanation:

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

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

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

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

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

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

r = 20 $\displaystyle r = 20$.

The radius of the given circle is 20.

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Example Question #4 : Area

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?

Possible Answers:

Systematic sampling

Stratified sampling

Cluster sampling

Convenience sampling

Correct answer:

Systematic 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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Example Question #5 : Area

What is the area of a circle that has a diameter of $\displaystyle 12$?

Possible Answers:

113.1 $\displaystyle 113.1$

452.4 $\displaystyle 452.4$

37.7 $\displaystyle 37.7$

92.6 $\displaystyle 92.6$

Correct answer:

113.1 $\displaystyle 113.1$

Explanation:

Recall how to find the area of a circle:

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

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

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

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

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

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TACHS Math : Area of a circle

Study concepts, example questions & explanations for TACHS Math

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Example Question #1 : Area

Example Question #3 : Area

Example Question #4 : Area

Example Question #5 : Area

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