Diameter

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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.

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.

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

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

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 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 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.

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

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