# Basic Geometry : Diameter

## Example Questions

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

Find the diameter of a circle that has a circumference of .

Explanation:

Recall how to find the circumference of a circle:

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

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

Simplify.

### Example Question #32 : How To Find The Length Of The Diameter

Find the diameter of a circle that has a circumference of .

Explanation:

Recall how to find the circumference of a circle:

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

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

Simplify.

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

Find the diameter of a circle that has a circumference of .

Explanation:

Recall how to find the circumference of a circle:

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

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

Simplify.

### Example Question #34 : How To Find The Length Of The Diameter

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

Explanation:

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

### Example Question #35 : 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 .

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.

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.

### Example Question #36 : 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 .

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.

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.

### Example Question #37 : 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 .

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.

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.

### Example Question #38 : 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 .

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.

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.

### Example Question #39 : 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 .

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.

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.

### Example Question #40 : 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 .