Basic Geometry : How to find circumference

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #41 : How To Find Circumference

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

Possible Answers:

Correct answer:

Explanation:

13

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.

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

Simplify.

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

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

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

Example Question #42 : How To Find Circumference

Find the circumference of a circle inscribed in a square that has a diagonal of .

Possible Answers:

Correct answer:

Explanation:

13

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.

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

Simplify.

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

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

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

Example Question #43 : How To Find Circumference

Find the circumference of a circle inscribed in a square that has a diagonal of .

Possible Answers:

Correct answer:

Explanation:

13

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.

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

Simplify.

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

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

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

Example Question #44 : How To Find Circumference

Find the circumference of a circle inscribed in a square that has a diagonal of .

Possible Answers:

Correct answer:

Explanation:

13

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.

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

Simplify.

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

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

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

Example Question #41 : How To Find Circumference

Find the circumference of a circle inscribed in a square that has a diagonal of .

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

13

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.

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

Simplify.

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

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

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

Example Question #46 : How To Find Circumference

Find the circumference of a circle inscribed in a square that has a diagonal of .

Possible Answers:

Correct answer:

Explanation:

13

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.

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

Simplify.

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

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

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

Example Question #47 : How To Find Circumference

Find the circumference of a circle inscribed in a square that has a diagonal of .

Possible Answers:

Correct answer:

Explanation:

13

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.

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

Simplify.

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

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

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

Example Question #48 : How To Find Circumference

Find the circumference of a circle inscribed in a square that has a diagonal of .

Possible Answers:

Correct answer:

Explanation:

13

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.

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

Simplify.

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

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

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

Example Question #49 : How To Find Circumference

Find the circumference of a circle inscribed in a square that has a diagonal of .

Possible Answers:

Correct answer:

Explanation:

13

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.

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

Simplify.

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

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

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

Example Question #241 : Radius

Find the circumference of a circle inscribed in a square that has a diagonal of .

Possible Answers:

Correct answer:

Explanation:

13

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.

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

Simplify.

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

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

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

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