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Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

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9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #46 : Diameter

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

Possible Answers:

$6\sqrt2$

$12\sqrt2$

$48\sqrt2$

$24\sqrt2$

Correct answer:

$24\sqrt2$

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.

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

$2(\text{side})^2=\text{Diagonal}^2$

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

$\text{side}=\sqrt{\frac{\text{Diagonal}^2}{2}}=\frac{\text{Diagonal}\sqrt2}{2}$

Substitute in the length of the diagonal to find the length of the square.

$\text{side}=\frac{48(\sqrt2)}{2}$

Simplify.

$\text{side}=24\sqrt2$

Now, recall the relationship between the diameter of the circle and the side of the square.

$\text{diameter}=\text{side}=24\sqrt2$

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Example Question #351 : Plane Geometry

Find the length of the diameter given the area is $16\pi$ .

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for area to solve for the radius and multiply by 2.

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

$r=\sqrt{\frac{16\pi}{\pi}}=\sqrt{16}=4$

d=2r=2*4=8

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Example Question #42 : Diameter

The circumference of a circle is equal to 251.33 units . Find the length of the diameter of this circle.

Possible Answers:

90 units

70 units

60 units

40 units

80 units

Correct answer:

80 units

Explanation:

There are two steps to finding the answer to this question. The first is to find the radius through the formula for the circumference of a circle.

$Area = 2 (\pi) (r)$

Then we plug in numbers and solve.

$251.33 = 2 (\pi) (r)$

$125.7 = \pi (r)$

40 = radius

Now that we have found the radius, we solve for diameter by doubling it, since..

Diameter = 2(Radius)

Therefore, the diameter is equal to 80 units .

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Example Question #352 : Circles

Find the length of the diameter given radius is 7.

Possible Answers:

$28\pi$

$49\pi$

$14\pi$

Correct answer:

Explanation:

To solve, simply use the formula for the diameter of a circle.

Recall that the diameter of a circle is twice the radius of the circle.

Given that the radius is seven, multiply it by 2 to solve for the diameter.

Thus,

$\\d=2r\\d=2*7\\d=14$ .

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Example Question #351 : Circles

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

Possible Answers:

$6\pi$

Correct answer:

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,

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

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

d=2r=2*3=6

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Example Question #352 : Plane Geometry

Find the diameter of a circle whose radius is 5.

Possible Answers:

$25\pi$

$10\pi$

Correct answer:

Explanation:

The diameter of a circle is the width from side to side going through the center on the circle. In other words, the diameter is twice the radius.

To solve, simply use the formula for the diameter of a circle and substitute in the known radius in question.

Thus,

r=5

d=2r=2*5=10

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Example Question #353 : Plane Geometry

Find the length of the diameter of a circle given a radius of 7.

Possible Answers:

$\14\pi$

$7\pi$

Correct answer:

Explanation:

The diameter of a circle is the width from side to side going through the center on the circle. In other words, the diameter is twice the radius.

To solve, simply use the formula for the diameter of a circle and substitute in the known radius in question.

Thus,

d=2r=2*7=14

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Example Question #353 : Circles

Penny recently moved into a Native American Teepee with a floor plan that is a perfect circle and encompasses $300\;ft^2$ . What would be the diameter of the circular floor plan for Penny's Teepee? Round your value to the nearest tenth.

Possible Answers:

$47.7\;ft$

$9.8\;ft$

$19.5\;ft$

$18.7\;ft$

$95.5\;ft$

Correct answer:

$19.5\;ft$

Explanation:

Since we already know the area of the circle, we can look at the equation for circular area to find the diameter:

$Area=\pi\cdot r^2$

$\\300\;ft^2=\pi\cdot r^2\\r^2=\frac{300\;ft^2}{\pi}=\frac{300\;ft^2}{3.14159}=95.49\;ft^2\\r=\sqrt{95.49\;ft^2}=9.77\;ft$

$diameter=2\cdot radius=2\cdot9.77\;ft=19.54\;ft\approx19.5\;ft$

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Example Question #354 : Plane Geometry

Find the length of the diameter of a circle with radius 100.

Possible Answers:

10000

$200\pi$

200

$10000\pi$

Correct answer:

200

Explanation:

To solve, simply use the formula for the diameter. Thus,

d=2r=2*100=200

Don't be fooled by large numbers, simply use the formula how you memorized it. Remember, diameter is just twice the radius.

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Example Question #354 : Circles

A circle has a circumference of $3\pi cm$ . What is the length of the circle's diameter?

Possible Answers:

9 cm

1.5 cm

6 cm

$\pi cm$

3 cm

Correct answer:

3 cm

Explanation:

The formula for the circumference of a circle is:

$C=\pi d$

Since the circumference is $3\pi$ :

$3\pi=\pi d$

We then solve for :

$\frac{3\pi}{\pi}=\frac{\pi d}{\pi}$

d=3

Therefore, the circle's diameter is 3 cm .

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Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #46 : Diameter

Example Question #351 : Plane Geometry

Example Question #42 : Diameter

Example Question #352 : Circles

Example Question #351 : Circles

Example Question #352 : Plane Geometry

Example Question #353 : Plane Geometry

Example Question #353 : Circles

Example Question #354 : Plane Geometry

Example Question #354 : Circles

All Basic Geometry Resources

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