How to find the length of the diameter - Math

Card 0 of 288

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$

Compare your answer with the correct one above

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

Compare your answer with the correct one above

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.

Compare your answer with the correct one above

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.

Compare your answer with the correct one above

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, .

Compare your answer with the correct one above

Question

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

Answer

$C = \pi d$

$36 \pi = \pi d$

Compare your answer with the correct one above

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}$$

Compare your answer with the correct one above

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 .

Compare your answer with the correct one above

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.

Compare your answer with the correct one above

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}$=14$

Compare your answer with the correct one above

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}$=10$

Compare your answer with the correct one above

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}$=100$

Compare your answer with the correct one above

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}$

Compare your answer with the correct one above

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}$

Compare your answer with the correct one above

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}$

Compare your answer with the correct one above

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}$

Compare your answer with the correct one above

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}$

Compare your answer with the correct one above

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}$

Compare your answer with the correct one above

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}$=78$

Compare your answer with the correct one above

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}$=992$

Compare your answer with the correct one above

Tap the card to reveal the answer