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Basic Geometry : Plane Geometry

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

Example Questions

Example Question #1 : Diameter

A circle has an area of $60\pi$ $\displaystyle 60\pi$ cm^2 $\displaystyle cm^2$. What is the circle's diameter?

Possible Answers:

$\displaystyle 60$$\displaystyle cm$

$2\sqrt{15}\pi$ $\displaystyle 2\sqrt{15}\pi$ $\displaystyle cm$

$4\sqrt{15}$ $\displaystyle 4\sqrt{15}$ $\displaystyle cm$

$2\sqrt{15}$ $\displaystyle 2\sqrt{15}$ $\displaystyle cm$

$\displaystyle 30$$\displaystyle cm$

Correct answer:

$4\sqrt{15}$ $\displaystyle 4\sqrt{15}$ $\displaystyle cm$

Explanation:

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

$60\pi = \pi r^2$ $\displaystyle 60\pi = \pi r^2$

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

$\displaystyle 60 = r^2$

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

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

To find the circle's diameter, multiply its radius by $\displaystyle 2$.

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

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Example Question #311 : Plane Geometry

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

Possible Answers:

$\displaystyle 12$ inches

$\displaystyle 10$ inches

$\displaystyle 14$ inches

$\displaystyle 20$ inches

$\displaystyle 17$ inches

Correct answer:

$\displaystyle 14$ inches

Explanation:

The diameter of a circle can be written as d=2r $\displaystyle d=2r$, where $\displaystyle r$ is the radius and $\displaystyle d$ is the diameter.

$\displaystyle (7) 2 = 14$

Therefore the diameter of the circle is 14 inches.

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Example Question #2 : Diameter

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

Possible Answers:

$6.25\pi$ $\displaystyle 6.25\pi$

$6\pi$ $\displaystyle 6\pi$

$25\pi$ $\displaystyle 25\pi$

$5\pi$ $\displaystyle 5\pi$

$12.5\pi$ $\displaystyle 12.5\pi$

Correct answer:

$6.25\pi$ $\displaystyle 6.25\pi$

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.

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

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Example Question #7 : Diameter

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

Possible Answers:

$\displaystyle 3$

$\displaystyle 12$

$\displaystyle 6$

$\displaystyle 5$

$\displaystyle 1$

Correct answer:

$\displaystyle 6$

Explanation:

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:

$A=\pi r^2$ $\displaystyle A=\pi r^2$

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

$9\pi=\pi r^2$ $\displaystyle 9\pi=\pi r^2$

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

9=r^2 $\displaystyle 9=r^2$

3=r $\displaystyle 3=r$

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

$\displaystyle D=2r=2(3)=6$

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Example Question #4 : Diameter

Find the diameter of a circle that has an area of $144\pi$ $\displaystyle 144\pi$.

Possible Answers:

144 $\displaystyle 144$

$\displaystyle 24$

$\displaystyle 12$

$24\pi$ $\displaystyle 24\pi$

Correct answer:

$\displaystyle 24$

Explanation:

Recall how to find the area of a circle:

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

Next, plug in the information given by the question.

$144\pi=\pi\times\text{radius}^2$ $\displaystyle 144\pi=\pi\times\text{radius}^2$

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

$\text{radius}^2=144$ $\displaystyle \text{radius}^2=144$

$\text{radius}=\sqrt{144}=12$ $\displaystyle \text{radius}=\sqrt{144}=12$

Now recall the relationship between the radius and the diameter.

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

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

$\text{diameter}=2\times 12 = 24$ $\displaystyle \text{diameter}=2\times 12 = 24$

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Example Question #311 : Circles

Find the diameter of a circle that has an area of $169\pi$ $\displaystyle 169\pi$.

Possible Answers:

$\displaystyle 26$

$26\pi$ $\displaystyle 26\pi$

$\displaystyle 52$

$\displaystyle 13$

Correct answer:

$\displaystyle 26$

Explanation:

Recall how to find the area of a circle:

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

Next, plug in the information given by the question.

$169\pi=\pi\times\text{radius}^2$ $\displaystyle 169\pi=\pi\times\text{radius}^2$

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

$\text{radius}^2=169$ $\displaystyle \text{radius}^2=169$

$\text{radius}=\sqrt{169}=13$ $\displaystyle \text{radius}=\sqrt{169}=13$

Now recall the relationship between the radius and the diameter.

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

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

$\text{diameter}=2\times 13 = 26$ $\displaystyle \text{diameter}=2\times 13 = 26$

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Example Question #312 : Circles

Find the diameter of a circle whose area is $49\pi$ $\displaystyle 49\pi$.

Possible Answers:

$\displaystyle 49$

$\displaystyle 14$

$7\pi$ $\displaystyle 7\pi$

$14\pi$ $\displaystyle 14\pi$

Correct answer:

$\displaystyle 14$

Explanation:

Recall how to find the area of a circle:

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

Next, plug in the information given by the question.

$49\pi=\pi\times\text{radius}^2$ $\displaystyle 49\pi=\pi\times\text{radius}^2$

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

$\text{radius}^2=49$ $\displaystyle \text{radius}^2=49$

$\text{radius}=\sqrt{49}=7$ $\displaystyle \text{radius}=\sqrt{49}=7$

Now recall the relationship between the radius and the diameter.

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

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

$\text{diameter}=2\times 7 = 14$ $\displaystyle \text{diameter}=2\times 7 = 14$

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Example Question #312 : Circles

Find the diameter of a circle whose area is $676\pi$ $\displaystyle 676\pi$.

Possible Answers:

$\displaystyle 13$

$\displaystyle 26$

104 $\displaystyle 104$

$\displaystyle 52$

Correct answer:

$\displaystyle 52$

Explanation:

Recall how to find the area of a circle:

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

Next, plug in the information given by the question.

$676\pi=\pi\times\text{radius}^2$ $\displaystyle 676\pi=\pi\times\text{radius}^2$

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

$\text{radius}^2=676$ $\displaystyle \text{radius}^2=676$

$\text{radius}=\sqrt{676}=26$ $\displaystyle \text{radius}=\sqrt{676}=26$

Now recall the relationship between the radius and the diameter.

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

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

$\text{diameter}=2\times 26 = 52$ $\displaystyle \text{diameter}=2\times 26 = 52$

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Example Question #14 : How To Find The Length Of The Diameter

Find the diameter of a circle whose area is $324\pi$ $\displaystyle 324\pi$.

Possible Answers:

$\displaystyle 36$

$\displaystyle 72$

$\displaystyle 9$

$\displaystyle 18$

Correct answer:

$\displaystyle 36$

Explanation:

Recall how to find the area of a circle:

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

Next, plug in the information given by the question.

$324\pi=\pi\times\text{radius}^2$ $\displaystyle 324\pi=\pi\times\text{radius}^2$

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

$\text{radius}^2=324$ $\displaystyle \text{radius}^2=324$

$\text{radius}=\sqrt{324}=18$ $\displaystyle \text{radius}=\sqrt{324}=18$

Now recall the relationship between the radius and the diameter.

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

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

$\text{diameter}=2\times 18 = 36$ $\displaystyle \text{diameter}=2\times 18 = 36$

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Example Question #12 : Diameter

Find the diameter of a circle whose area is $289\pi$ $\displaystyle 289\pi$.

Possible Answers:

$\displaystyle 34$

8.5 $\displaystyle 8.5$

$\displaystyle 68$

$\displaystyle 17$

Correct answer:

$\displaystyle 34$

Explanation:

Recall how to find the area of a circle:

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

Next, plug in the information given by the question.

$289\pi=\pi\times\text{radius}^2$ $\displaystyle 289\pi=\pi\times\text{radius}^2$

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

$\text{radius}^2=289$ $\displaystyle \text{radius}^2=289$

$\text{radius}=\sqrt{289}=17$ $\displaystyle \text{radius}=\sqrt{289}=17$

Now recall the relationship between the radius and the diameter.

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

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

$\text{diameter}=2\times 17 = 34$ $\displaystyle \text{diameter}=2\times 17 = 34$

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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #1 : Diameter

Example Question #311 : Plane Geometry

Example Question #2 : Diameter

Example Question #7 : Diameter

Example Question #4 : Diameter

Example Question #311 : Circles

Example Question #312 : Circles

Example Question #312 : Circles

Example Question #14 : How To Find The Length Of The Diameter

Example Question #12 : Diameter

All Basic Geometry Resources

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