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Basic Geometry : How to find the length of the diameter

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #31 : Diameter

Find the diameter of a circle that has a circumference of $78\pi$ .

Possible Answers:

146

$39\pi$

$\frac{78}{\pi}$

Correct answer:

Explanation:

Recall how to find the circumference of a circle:

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

If we divide both sides of the equation by $\pi$ , then we can write the following equation:

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

We can substitute in the given information to find the diameter of the circle in the question.

$\text{Diameter}=\frac{78\pi}{\pi}$

Simplify.

$\text{Diameter}=78$

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Example Question #31 : How To Find The Length Of The Diameter

Find the diameter of a circle that has a circumference of $992\pi$ .

Possible Answers:

$\frac{496}{\pi}$

$1188\pi$

$\frac{992}{\pi}$

992

Correct answer:

992

Explanation:

Recall how to find the circumference of a circle:

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

If we divide both sides of the equation by $\pi$ , then we can write the following equation:

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

We can substitute in the given information to find the diameter of the circle in the question.

$\text{Diameter}=\frac{992\pi}{\pi}$

Simplify.

$\text{Diameter}=992$

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Example Question #333 : Circles

Find the diameter of a circle that has a circumference of $1000\pi$ .

Possible Answers:

1000

100

500

$\frac{1000}{\pi}$

Correct answer:

1000

Explanation:

Recall how to find the circumference of a circle:

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

If we divide both sides of the equation by $\pi$ , then we can write the following equation:

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

We can substitute in the given information to find the diameter of the circle in the question.

$\text{Diameter}=\frac{1000\pi}{\pi}$

Simplify.

$\text{Diameter}=1000$

Report an Error

Example Question #31 : How To Find The Length Of The Diameter

If the radius of a circle is 7cm , what is the diameter?

Possible Answers:

16cm

9cm

21cm

49cm

14cm

Correct answer:

14cm

Explanation:

The radius of a circle is half of the diameter, therefore:

2(radius) = diameter

2(7) = diameter

14cm = diameter

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Example Question #33 : Diameter

Find the length of the diameter of a circle inscribed in a square that has a diagonal of $3\sqrt2$ .

Possible Answers:

$3\pi$

$3\sqrt2$

Correct answer:

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.

$\text{side}=\frac{3\sqrt2(\sqrt2)}{2}$

Simplify.

$\text{side}=3$

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

$\text{diameter}=\text{side}=3$

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Example Question #33 : How To Find The Length Of The Diameter

Find the length of the diameter of a circle inscribed in a square that has a diagonal of $2\sqrt2$ .

Possible Answers:

$4\pi$

$2\pi$

Correct answer:

Explanation:

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.

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

Simplify.

$\text{side}=2$

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

$\text{diameter}=\text{side}=2$

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Example Question #342 : Basic Geometry

Find the length of the diameter of a circle inscribed in a square that has a diagonal of $4\sqrt2$ .

Possible Answers:

$16\pi$

$2\pi$

Correct answer:

Explanation:

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.

$\text{side}=\frac{4\sqrt2(\sqrt2)}{2}$

Simplify.

$\text{side}=4$

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

$\text{diameter}=\text{side}=4$

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Example Question #343 : Basic Geometry

Find the length of the diameter of a circle inscribed in a square that has a diagonal of $5\sqrt2$ .

Possible Answers:

$10\pi$

$5\sqrt2$

$\frac{5\sqrt2}{2}$

Correct answer:

Explanation:

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.

$\text{side}=\frac{5\sqrt2(\sqrt2)}{2}$

Simplify.

$\text{side}=5$

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

$\text{diameter}=\text{side}=5$

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Example Question #344 : Basic Geometry

Find the length of the diameter of a circle inscribed in a square that has a diagonal of $6\sqrt2$ .

Possible Answers:

$3\pi$

$12\pi$

Correct answer:

Explanation:

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.

$\text{side}=\frac{6\sqrt2(\sqrt2)}{2}$

Simplify.

$\text{side}=6$

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

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

Report an Error

Example Question #345 : Basic Geometry

Find the length of the diameter of a circle inscribed in a square that has a diagonal of $7\sqrt2$ .

Possible Answers:

$\frac{7}{2}$

$7\sqrt2$

Correct answer:

Explanation:

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.

$\text{side}=\frac{7\sqrt2(\sqrt2)}{2}$

Simplify.

$\text{side}=7$

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

$\text{diameter}=\text{side}=7$

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Basic Geometry : How to find the length of the diameter

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #31 : Diameter

Example Question #31 : How To Find The Length Of The Diameter

Example Question #333 : Circles

Example Question #31 : How To Find The Length Of The Diameter

Example Question #33 : Diameter

Example Question #33 : How To Find The Length Of The Diameter

Example Question #342 : Basic Geometry

Example Question #343 : Basic Geometry

Example Question #344 : Basic Geometry

Example Question #345 : Basic Geometry

All Basic Geometry Resources

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