Geometry - How to find the length of the diameter

A circle has a radius of 7 inches. What is the diameter of the circle?

inches

Explanation

The diameter of a circle can be written as , where is the radius and is the diameter.

Therefore the diameter of the circle is 14 inches.

Two legs of a right triangle measure 3 and 4, respectively. What is the area of the circle that circumscribes the triangle?

$6.25\pi$

$6\pi$

$5\pi$

$25\pi$

$12.5\pi$

Explanation

For the circle to contain all 3 vertices, the hypotenuse must be the diameter of the circle. The hypotenuse, and therefore the diameter, is 5, since this must be a 3-4-5 right triangle.

The equation for the area of a circle is A = πr2.

$A=\pi (5/2)^2=6.25\pi$

The perimeter of a circle is 36 π. What is the diameter of the circle?

Explanation

The perimeter of a circle = 2 πr = πd

Therefore d = 36

Find the diameter of a circle whose area is $3025\pi$ .

Explanation

Recall how to find the area of a circle:

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

Next, plug in the information given by the question.

$3025\pi=\pi\times\text{radius}^2$

From this, we can see that we can solve for the radius.

$\text{radius}^2=3025$

$\text{radius}=\sqrt{3025}=55$

Now recall the relationship between the radius and the diameter.

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

Plug in the value of the radius to find the diameter.

$\text{diameter}=2\times 55 = 110$

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

$\frac{12}{\pi}$

$\frac{6}{\pi}$

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.

$\text{Diameter}=\frac{12}{\pi}$

Find the length of the diameter of a circle given an area of $9\pi$ .

$6\pi$

Explanation

To solve, simply use the formula for the area to find the length of the radius and then multiply that by 2 to find the diameter. Thus,

$A=\pi{r^2}\Rightarrow r=\sqrt{\frac{A}{\pi}}$

$r=\sqrt{\frac{9\pi}{\pi}}=\sqrt9=3$

The area of a circle is $25 \pi \enspace in^2$ . What is the length of its diameter?

Explanation

The area of a circle is $\pi r^2$ . In this case, . Taking the square root, the radius has a length of 5. To find the diameter, multiply by 2. Two times five is 10, so the diameter has a length of 10.

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

$18\sqrt2$

$54\sqrt2$

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.

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