Basic Geometry : How to find the length of the diameter

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #51 : How To Find The Length Of The Diameter

Find the diameter of a circle whose radius is 5.

Possible Answers:

\(\displaystyle 10\pi\)

\(\displaystyle 25\)

\(\displaystyle 10\)

\(\displaystyle 25\pi\)

Correct answer:

\(\displaystyle 10\)

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,

\(\displaystyle r=5\)

\(\displaystyle d=2r=2*5=10\)

Example Question #352 : Circles

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

Possible Answers:

\(\displaystyle 14\)

\(\displaystyle 49\)

\(\displaystyle 7\pi\)

\(\displaystyle \14\pi\)

Correct answer:

\(\displaystyle 14\)

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,

\(\displaystyle d=2r=2*7=14\)

Example Question #354 : Basic Geometry

 

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

Possible Answers:

\(\displaystyle 95.5\;ft\)

\(\displaystyle 18.7\;ft\)

\(\displaystyle 19.5\;ft\)

\(\displaystyle 9.8\;ft\)

\(\displaystyle 47.7\;ft\)

Correct answer:

\(\displaystyle 19.5\;ft\)

Explanation:

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

\(\displaystyle Area=\pi\cdot r^2\)

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

\(\displaystyle diameter=2\cdot radius=2\cdot9.77\;ft=19.54\;ft\approx19.5\;ft\)

Example Question #353 : Circles

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

Possible Answers:

\(\displaystyle 10000\pi\)

\(\displaystyle 200\pi\)

\(\displaystyle 10000\)

\(\displaystyle 200\)

Correct answer:

\(\displaystyle 200\)

Explanation:

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

\(\displaystyle d=2r=2*100=200\)

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

Example Question #354 : Basic Geometry

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

Possible Answers:

\(\displaystyle 6 cm\)

\(\displaystyle \pi cm\)

\(\displaystyle 1.5 cm\)

\(\displaystyle 9 cm\)

\(\displaystyle 3 cm\)

Correct answer:

\(\displaystyle 3 cm\)

Explanation:

The formula for the circumference of a circle is:

\(\displaystyle C=\pi d\)

Since the circumference is \(\displaystyle 3\pi\):

\(\displaystyle 3\pi=\pi d\)

We then solve for \(\displaystyle d\):

\(\displaystyle \frac{3\pi}{\pi}=\frac{\pi d}{\pi}\)

\(\displaystyle d=3\)

Therefore, the circle's diameter is \(\displaystyle 3 cm\).

Example Question #54 : Diameter

A circle has an area of \(\displaystyle 3 \pi cm^2\). What is the diameter of the circle?

Possible Answers:

\(\displaystyle \sqrt{3}cm\)

\(\displaystyle 3 cm\)

\(\displaystyle 2\sqrt{3}cm\)

\(\displaystyle 3\sqrt{2}cm\)

\(\displaystyle 3\pi cm\)

Correct answer:

\(\displaystyle 2\sqrt{3}cm\)

Explanation:

The formula for the area of a circle is:

\(\displaystyle A=\pi r^2\)

Since we know the area is \(\displaystyle 3\pi\), we plug that in to solve for the radius:

\(\displaystyle 3\pi=\pi r^2\)

\(\displaystyle \frac{3\pi}{\pi}=\frac{\pi r^2}{\pi}\)

\(\displaystyle 3=r^2\)

\(\displaystyle r=\sqrt{3}\)

Now that we know the radius, we simply double it to find the diameter:

\(\displaystyle d=2\sqrt{3}\)

So the diameter of the circle is \(\displaystyle 2\sqrt{3}cm\).

 

Example Question #361 : Basic Geometry

From the center of a circle playing field to the edge is 25 yards. This is called the radius. What is the length of the diameter of the field?

Possible Answers:

\(\displaystyle 40\ Yards\)

\(\displaystyle 12.5\ Yards\)

\(\displaystyle 50\ Yards\)

\(\displaystyle 100\ Yards\)

\(\displaystyle 25\ Yards\)

Correct answer:

\(\displaystyle 50\ Yards\)

Explanation:

To find the diameter of a circle, it is from one side of the circle through the center of the circle to the other side. Or if the radius is from the center of a circle to the edge, the diameter must be twice the radius.

\(\displaystyle d=2r\)

Since the information given is the radius of the circle we know that \(\displaystyle r=25\).

Substituting the radius into the above equation we can solve for the diameter.

\(\displaystyle \\d=2(25) \\d=50\)

Therfore the diameter of this circle is double 25 yards which would be 50 yards.

Example Question #361 : Circles

The top of a can has a radius of 5cms. What is the length of the diameter of the can?

Possible Answers:

\(\displaystyle 20cms\)

\(\displaystyle 12.5cms\)

\(\displaystyle 5cms\)

\(\displaystyle 15cms\)

\(\displaystyle 10cms\)

Correct answer:

\(\displaystyle 10cms\)

Explanation:

To find the diameter of a circle, it is from one side of the circle through the center of the circle to the other side. Or if the radius is from the center of a circle to the edge, the diameter must be twice the radius.

\(\displaystyle d=2r\)

Since the information given is the radius of the circle we know that \(\displaystyle r=5\).

Substituting the radius into the above equation we can solve for the diameter.

\(\displaystyle \\d=2(5) \\d=10\)

Therfore the diameter of this circle is double 5cms which would be 10cms.

Example Question #361 : Basic Geometry

A circular pool has a circumference of 27 meters. What the diameter of the pool?

Possible Answers:

\(\displaystyle 10\hspace{1mm} meters\)

\(\displaystyle 15\hspace{1mm} meters\)

\(\displaystyle 15.4\hspace{1mm} meters\)

\(\displaystyle 84.8\hspace{1mm} meters\)

\(\displaystyle 8.6\hspace{1mm} meters\)

Correct answer:

\(\displaystyle 8.6\hspace{1mm} meters\)

Explanation:

We find the circumference of circles with the relationship \(\displaystyle C=\pi *D\), where D is diameter.

Since we are given the circumference of the pool, solve for D by dividing both sides by \(\displaystyle \pi\).

\(\displaystyle D=\frac{C}{\pi}=\frac{27meters}{\pi} =\mathbf{8.6\hspace{1mm}meters}\)

Example Question #54 : How To Find The Length Of The Diameter

If the radius of a circle is 7cm, what is the diameter?

Possible Answers:

\(\displaystyle 4cm\)

\(\displaystyle 49cm\)

\(\displaystyle 14cm\)

\(\displaystyle 3.5cm\)

\(\displaystyle 7cm\)

Correct answer:

\(\displaystyle 14cm\)

Explanation:

The radius is half of the diameter.

\(\displaystyle 2r=d\)

\(\displaystyle 2(7cm )=d\)

\(\displaystyle d=14cm\)

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