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Basic Geometry : Basic Geometry

Study concepts, example questions & explanations for Basic Geometry

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All Basic Geometry Resources

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

Example Questions

Example Question #221 : Basic Geometry

Find the circumference of a circle that is inscribed in a square that has side lengths of .

Possible Answers:

$10\pi$

$25\pi$

$\frac{25\pi}{4}$

$5\pi$

Correct answer:

$5\pi$

Explanation:

Notice that when a circle is inscribed in a square, the side length of the square is also the diameter of the circle.

Recall how to find the circumference of a circle:

$\text{Circumference}=\text{Diameter}\times\pi$

Plug in the given diameter to find the circumference.

$\text{Circumference}=5\pi$

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Example Question #221 : Basic Geometry

Find the circumference of a circle that is inscribed in a square that has side lengths of .

Possible Answers:

$9\pi$

$6\pi$

$18\pi$

$12\pi$

Correct answer:

$6\pi$

Explanation:

Notice that when a circle is inscribed in a square, the side length of the square is also the diameter of the circle.

Recall how to find the circumference of a circle:

$\text{Circumference}=\text{Diameter}\times\pi$

Plug in the given diameter to find the circumference.

$\text{Circumference}=6\pi$

Report an Error

Example Question #222 : Radius

Find the circumference of a circle that is inscribed in a square with side lengths of .

Possible Answers:

$\frac{49\pi}{4}$

$14\pi$

$7\pi$

$49\pi$

Correct answer:

$7\pi$

Explanation:

Notice that when a circle is inscribed in a square, the side length of the square is also the diameter of the circle.

Recall how to find the circumference of a circle:

$\text{Circumference}=\text{Diameter}\times\pi$

Plug in the given diameter to find the circumference.

$\text{Circumference}=7\pi$

Report an Error

Example Question #223 : Basic Geometry

Find the circumference of a circle that is inscribed inside a square with side lengths of .

Possible Answers:

$16\pi$

$64\pi$

$8\pi$

Correct answer:

$8\pi$

Explanation:

Notice that when a circle is inscribed in a square, the side length of the square is also the diameter of the circle.

Recall how to find the circumference of a circle:

$\text{Circumference}=\text{Diameter}\times\pi$

Plug in the given diameter to find the circumference.

$\text{Circumference}=8\pi$

Report an Error

Example Question #225 : Circles

Find the circumference of a circle that is inscribed inside a square with side lengths of .

Possible Answers:

$3\pi$

$81\pi$

$9\pi$

$18\pi$

Correct answer:

$9\pi$

Explanation:

Notice that when a circle is inscribed in a square, the side length of the square is also the diameter of the circle.

Recall how to find the circumference of a circle:

$\text{Circumference}=\text{Diameter}\times\pi$

Plug in the given diameter to find the circumference.

$\text{Circumference}=9\pi$

Report an Error

Example Question #224 : Basic Geometry

Find the circumference of a circle that is inscribed in a square with side lengths of .

Possible Answers:

$5\pi$

$20\pi$

$25\pi$

$10\pi$

Correct answer:

$10\pi$

Explanation:

Notice that when a circle is inscribed in a square, the side length of the square is also the diameter of the circle.

Recall how to find the circumference of a circle:

$\text{Circumference}=\text{Diameter}\times\pi$

Plug in the given diameter to find the circumference.

$\text{Circumference}=10\pi$

Report an Error

Example Question #225 : Basic Geometry

Find the circumference of a circle that is inscribed in a square with side lengths of .

Possible Answers:

$36\pi$

$144\pi$

$12\pi$

Correct answer:

$12\pi$

Explanation:

Notice that when a circle is inscribed in a square, the side length of the square is also the diameter of the circle.

Recall how to find the circumference of a circle:

$\text{Circumference}=\text{Diameter}\times\pi$

Plug in the given diameter to find the circumference.

$\text{Circumference}=12\pi$

Report an Error

Example Question #226 : Basic Geometry

Find the circumference of a circle inscribed in a square with side lengths of .

Possible Answers:

$26\pi$

$39\pi$

$42\pi$

$13\pi$

Correct answer:

$13\pi$

Explanation:

Notice that when a circle is inscribed in a square, the side length of the square is also the diameter of the circle.

Recall how to find the circumference of a circle:

$\text{Circumference}=\text{Diameter}\times\pi$

Plug in the given diameter to find the circumference.

$\text{Circumference}=13\pi$

Report an Error

Example Question #227 : Basic Geometry

Find the circumference of a circle that is inscribed in a square with side lengths of .

Possible Answers:

$121\pi$

$11\pi$

$22\pi$

Correct answer:

$11\pi$

Explanation:

Notice that when a circle is inscribed in a square, the side length of the square is also the diameter of the circle.

Recall how to find the circumference of a circle:

$\text{Circumference}=\text{Diameter}\times\pi$

Plug in the given diameter to find the circumference.

$\text{Circumference}=11\pi$

Report an Error

Example Question #230 : Radius

Find the circumference of a circle that is inscribed in a square with a diagonal of $100\sqrt2$ .

Possible Answers:

$50\pi$

$100\pi$

Cannot be determined

$10\pi$

Correct answer:

$100\pi$

Explanation:

When you draw out the circle that is inscribed in a square, you should notice two things. The first thing you should notice is that the diagonal of the square is also the hypotenuse of a right isosceles triangle that has the side lengths of the square as its legs. The second thing you should notice is that the diameter of the circle has the same length as the length of one side of the square.

First, use the Pythagorean theorem to find the length of a side of the square.

$\text{Diagonal}^2=\text{side}^2+\text{side}^2$

$2(\text{side})^2=\text{Diagonal}^2$

$\text{side}^2=\frac{\text{Diagonal}^2}{2}$

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Substitute in the length of the diagonal to find the length of the square.

$\text{side}=\frac{100\sqrt2(\sqrt2)}{2}$

Simplify.

$\text{side}=100$

Now, recall the relationship between the diameter of the circle and the side of the square.

$\text{diameter}=\text{side}=100$

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

$\text{Circumference}=\pi\times\text{diameter}$

Substitute in the diameter you just found to find the circumference.

$\text{Circumference}=100\pi$

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Basic Geometry : Basic Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #221 : Basic Geometry

Example Question #221 : Basic Geometry

Example Question #222 : Radius

Example Question #223 : Basic Geometry

Example Question #225 : Circles

Example Question #224 : Basic Geometry

Example Question #225 : Basic Geometry

Example Question #226 : Basic Geometry

Example Question #227 : Basic Geometry

Example Question #230 : Radius

All Basic Geometry Resources

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