Diameter - Basic Geometry

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Question

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

Answer

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.

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

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Question

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

Answer

The perimeter of a circle = 2 πr = πd

Therefore d = 36

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Question

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

Answer

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.

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Question

If the area of a circle is $9\pi$ , what is its diameter?

Answer

Before we can find the diameter of this circle, we need to find its radius. We need to use the formula for the area of a cirlce:

$A=\pi r^2$

Given that the area is $9\pi$ , we can find the radius

$9\pi=\pi r^2$

cancel the pi and then square root it to find 'r'.

Now that the radius is found, we can find the diamater by multiplying it by 2.

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Question

The area of a circle is $9\pi ; in^{2}$ . What is its diameter?

Answer

First solve for the radius:

$A=\pi r^{2} = 9\pi$

Note that , where is the radius and is the diameter.

Therefore, .

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Question

Give the diameter of a circle whose circumference is $36 \pi$ .

Answer

$C = \pi d$

$36 \pi = \pi d$

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Question

A circle has an area of $60\pi$ . What is the circle's diameter?

Answer

The area of a circle is given by the equation $A = \pi r^2$ , where is the area and is the radius. Use the given area in this equation and solve for to find the circle's radius.

$60\pi = \pi r^2$

$\frac{(60\pi)}{\pi} = \frac{(\pi r^2)}{\pi}$

$\sqrt{60} = \sqrt{r^2}$

$r = \sqrt{60} = 2\sqrt{15}$

To find the circle's diameter, multiply its radius by .

$2\sqrt{15} * 2 = 4\sqrt{15}$

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Question

Two circles have only one point in common. Both circles have radii of . If point is on the first circle and point is on the second circle, what is longest possible distance of line ?

Answer

The first step is to sketch two circles touching at a single point. In order to maximize the length of , the point and the point would need to be on opposite ends, as shown in the diagram. If the radius of a circle is , then the diameter would be . Therefore, the length of would be .

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Question

What is the name of the segment in green?

Answer

The diameter is the maximum distance between two points on a circle's perimeter. The diameter passes through the circle's center.

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Question

Find the diameter of a circle that has a circumference of $14\pi$ .

Answer

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.

$\text{Diameter}=\frac{14\pi}{\pi}$

Simplify.

$\text{Diameter}=14$

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Question

Find the diameter of a circle that has a circumference of $10\pi$ .

Answer

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.

$\text{Diameter}=\frac{10\pi}{\pi}$

Simplify.

$\text{Diameter}=10$

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Question

Find the diameter of a circle that has a circumference of $100\pi$ .

Answer

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.

$\text{Diameter}=\frac{100\pi}{\pi}$

Simplify.

$\text{Diameter}=100$

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Question

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

Answer

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.

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

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Question

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

Answer

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.

$\text{Diameter}=\frac{100}{\pi}$

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Question

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

Answer

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.

$\text{Diameter}=\frac{18}{\pi}$

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Question

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

Answer

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.

$\text{Diameter}=\frac{91}{\pi}$

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Question

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

Answer

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.

$\text{Diameter}=\frac{45}{\pi}$

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Question

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

Answer

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.

$\text{Diameter}=\frac{12.4}{\pi}$

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Question

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

Answer

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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Question

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

Answer

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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