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Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

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9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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Example Question #51 : How To Find The Area Of A Circle

Find the area of a circle that has a radius of .

Possible Answers:

$44\pi$

$484\pi$

$144\pi$

$626\pi$

Correct answer:

$484\pi$

Explanation:

Use the following formula to find the area of a circle:

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

For the circle in question, plug in the given radius to find the area.

$\text{Area}=\pi \times (22)^2=484\pi$

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Example Question #51 : Plane Geometry

Find the area of a circle that has a radius of 1.2 .

Possible Answers:

$1.3\pi$

$3.6\pi$

$2.4\pi$

$1.44\pi$

Correct answer:

$1.44\pi$

Explanation:

Use the following formula to find the area of a circle:

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

For the circle in question, plug in the given radius to find the area.

Remember when multiplying decimals together first move the decimal over so that the number is a whole integer.

$1.2\rightarrow 12$

Now we multiple the integers together.

$1.2\cdot 1.2\rightarrow 12\cdot 12=144$

From here, we need to move the decimal place back. In this particular problem we moved the decimal over one time for each number for a total of two decimal places.

Therefore our r^2 becomes,

$144\rightarrow 1.44$ .

$\text{Area}=\pi \times (1.2)^2=1.44\pi$

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Example Question #52 : Plane Geometry

Find the area of a circle with the radius of 6.3 .

Possible Answers:

$35.39\pi$

$30.09\pi$

$42.19\pi$

$39.69\pi$

Correct answer:

$39.69\pi$

Explanation:

Use the following formula to find the area of a circle:

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

For the circle in question, plug in the given radius to find the area.

Remember when multiplying decimals together first move the decimal over so that the number is a whole integer.

$6.3\rightarrow 63$

Now we multiple the integers together.

$6.3\cdot 6.3\rightarrow 63\cdot 63=3669$

From here, we need to move the decimal place back. In this particular problem we moved the decimal over one time for each number for a total of two decimal places.

Therefore our r^2 becomes,

$3669\rightarrow 36.69$ .

$\text{Area}=\pi \times (6.3)^2=36.69\pi$

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Example Question #52 : How To Find The Area Of A Circle

Find the area of a circle whose radius is .

Possible Answers:

$6\pi$

$9\pi$

$12\pi$

$3\pi$

Correct answer:

$9\pi$

Explanation:

To find area, you must used the following equation.

$A=\pi{r^2}=\pi(3)^2=9\pi$

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Example Question #51 : Radius

find the area of a circle given the radius is .

Possible Answers:

$16\pi$

$2\pi$

$8\pi$

$4\pi$

Correct answer:

$4\pi$

Explanation:

To find area, use the following formula:

$A=\pi{r^2}=\pi(2^2)=4\pi$

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Example Question #51 : Circles

A circle is inscribed in a square that has an area of . What is the area of the circle?

Possible Answers:

$64\pi$

$16\pi$

The area of the circle cannot be determined.

Correct answer:

$16\pi$

Explanation:

The following figure illustrates the situation put forth by the question.

Notice that the diameter of the circle has the same length as a side of the square.

First, find the side length of the square.

$\text{Area of Square}=\text{side length}^2$

$\text{side length}=\sqrt{\text{Area of square}}$

Plug in the value given for the area to find the side length.

$\text{side length}=\sqrt{64}=8$

$\text{side length}=\text{diameter}=8$

Now, recall how to find the area of a circle.

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

We also know the relationship between the radius and the diameter.

$\text{diameter}=2\times\text{radius}$

Use the value you found earlier for the diameter to get the length of the radius.

$\text{radius}=\frac{\text{diameter}}{2}$

$\text{radius}=\frac{8}{2}=4$

Plug this value for the radius back into the equation for the area of a circle.

$\text{Area}=\pi \times 4^2=16\pi$

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Example Question #57 : Circles

A circle is inscribed in a square that has an area of 144 . What is the area of the circle?

Possible Answers:

The area of the circle cannot be determined.

$144\pi$

$64\pi$

$36\pi$

Correct answer:

$36\pi$

Explanation:

The following figure illustrates the situation put forth by the question.

Notice that the diameter of the circle has the same length as a side of the square.

First, find the side length of the square.

$\text{Area of Square}=\text{side length}^2$

$\text{side length}=\sqrt{\text{Area of square}}$

Plug in the value given for the area to find the side length.

$\text{side length}=\sqrt{144}=12$

$\text{side length}=\text{diameter}=12$

Now, recall how to find the area of a circle.

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

We also know the relationship between the radius and the diameter.

$\text{diameter}=2\times\text{radius}$

Use the value you found earlier for the diameter to get the length of the radius.

$\text{radius}=\frac{\text{diameter}}{2}$

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

Plug this value for the radius back into the equation for the area of a circle.

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

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Example Question #58 : Circles

A circle is inscribed in a square that has an area of . What is the area of the circle?

Possible Answers:

$9\pi$

$81\pi$

$3\pi$

Correct answer:

$9\pi$

Explanation:

The following figure illustrates the situation put forth by the question.

Notice that the diameter of the circle has the same length as a side of the square.

First, find the side length of the square.

$\text{Area of Square}=\text{side length}^2$

$\text{side length}=\sqrt{\text{Area of square}}$

Plug in the value given for the area to find the side length.

$\text{side length}=\sqrt{36}=6$

$\text{side length}=\text{diameter}=6$

Now, recall how to find the area of a circle.

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

We also know the relationship between the radius and the diameter.

$\text{diameter}=2\times\text{radius}$

Use the value you found earlier for the diameter to get the length of the radius.

$\text{radius}=\frac{\text{diameter}}{2}$

$\text{radius}=\frac{6}{2}=3$

Plug this value for the radius back into the equation for the area of a circle.

$\text{Area}=\pi \times 3^2=9\pi$

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Example Question #59 : Circles

A circle is inscribed in a square that has an area of 576 . What is the area of the circle?

Possible Answers:

$121\pi$

$144\pi$

Correct answer:

$144\pi$

Explanation:

The following figure illustrates the situation put forth by the question.

Notice that the diameter of the circle has the same length as a side of the square.

First, find the side length of the square.

$\text{Area of Square}=\text{side length}^2$

$\text{side length}=\sqrt{\text{Area of square}}$

Plug in the value given for the area to find the side length.

$\text{side length}=\sqrt{576}=24$

$\text{side length}=\text{diameter}= 24$

Now, recall how to find the area of a circle.

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

We also know the relationship between the radius and the diameter.

$\text{diameter}=2\times\text{radius}$

Use the value you found earlier for the diameter to get the length of the radius.

$\text{radius}=\frac{\text{diameter}}{2}$

$\text{radius}=\frac{24}{2}=12$

Plug this value for the radius back into the equation for the area of a circle.

$\text{Area}=\pi \times 12^2=144\pi$

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Example Question #60 : Circles

A circle is inscribed in a square that has an area of 256 . What is the area of the circle?

Possible Answers:

$64\pi$

$128\pi$

$192\pi$

$200\pi$

Correct answer:

$64\pi$

Explanation:

The following figure illustrates the situation put forth by the question.

Notice that the diameter of the circle has the same length as a side of the square.

First, find the side length of the square.

$\text{Area of Square}=\text{side length}^2$

$\text{side length}=\sqrt{\text{Area of square}}$

Plug in the value given for the area to find the side length.

$\text{side length}=\sqrt{256}=16$

$\text{side length}=\text{diameter}=16$

Now, recall how to find the area of a circle.

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

We also know the relationship between the radius and the diameter.

$\text{diameter}=2\times\text{radius}$

Use the value you found earlier for the diameter to get the length of the radius.

$\text{radius}=\frac{\text{diameter}}{2}$

$\text{radius}=\frac{16}{2}=8$

Plug this value for the radius back into the equation for the area of a circle.

$\text{Area}=\pi \times 8^2=64\pi$

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Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #51 : How To Find The Area Of A Circle

Example Question #51 : Plane Geometry

Example Question #52 : Plane Geometry

Example Question #52 : How To Find The Area Of A Circle

Example Question #51 : Radius

Example Question #51 : Circles

Example Question #57 : Circles

Example Question #58 : Circles

Example Question #59 : Circles

Example Question #60 : Circles

All Basic Geometry Resources

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