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Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #361 : Circles

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

Possible Answers:

3 cm

$2\sqrt{3}cm$

$3\sqrt{2}cm$

$\sqrt{3}cm$

$3\pi cm$

Correct answer:

$2\sqrt{3}cm$

Explanation:

The formula for the area of a circle is:

$A=\pi r^2$

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

$3\pi=\pi r^2$

$\frac{3\pi}{\pi}=\frac{\pi r^2}{\pi}$

3=r^2

$r=\sqrt{3}$

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

$d=2\sqrt{3}$

So the diameter of the circle is $2\sqrt{3}cm$ .

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Example Question #362 : Circles

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:

$100\ Yards$

$25\ Yards$

$40\ Yards$

$12.5\ Yards$

$50\ Yards$

Correct answer:

$50\ Yards$

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.

d=2r

Since the information given is the radius of the circle we know that r=25 .

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

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

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

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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:

20cms

12.5cms

5cms

15cms

10cms

Correct answer:

10cms

Explanation:

d=2r

Since the information given is the radius of the circle we know that r=5 .

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

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

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

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

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

Possible Answers:

$15.4\hspace{1mm} meters$

$10\hspace{1mm} meters$

$15\hspace{1mm} meters$

$84.8\hspace{1mm} meters$

$8.6\hspace{1mm} meters$

Correct answer:

$8.6\hspace{1mm} meters$

Explanation:

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

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

$D=\frac{C}{\pi}=\frac{27meters}{\pi} =\mathbf{8.6\hspace{1mm}meters}$

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Example Question #361 : Circles

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

Possible Answers:

3.5cm

49cm

14cm

4cm

7cm

Correct answer:

14cm

Explanation:

The radius is half of the diameter.

2r=d

2(7cm )=d

d=14cm

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Example Question #362 : Circles

The area of a circle is $196\pi$ inches^2 . What is the diameter?

Possible Answers:

$32\ in$

$14\ in$

$16\ in$

$28\ in$

$22\ in$

Correct answer:

$28\ in$

Explanation:

To find the diameter, we must first find the radius using the formula to find a circle's area.

$\pi r^2=area$

We have the area, so we have to work backwards.

$\pi r^2=196\pi$

Divide both sides by $\pi$

r^2=196

Take the square root of both sides.

$\sqrt{r^2}=\sqrt{196}$

r=14 inches

Now, since you have the radius, you have to double it to get the diameter.

diameter = 28 inches

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Example Question #61 : Diameter

The area of a circle is $81 \pi \enspace un^2$ . What is the diameter?

Possible Answers:

4.5 un

81 un

18 un

9 un

Correct answer:

18 un

Explanation:

The area of a circle is $\pi r^2$ , which means that in this circle, the radius squared is 81. The square root of 81 is 9, which means that the radius is 9. The diameter is just twice the length of the radius, so in this case 9 times 2, which is 18.

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Example Question #62 : Diameter

The area of a circle is $25 \pi \enspace in^2$ . What is the length of its diameter?

Possible Answers:

5 in

10 in

2.5 in

25 in

50 in

Correct answer:

10 in

Explanation:

The area of a circle is $\pi r^2$ . In this case, r ^2 = 25 . Taking the square root, the radius has a length of 5. To find the diameter, multiply by 2. Two times five is 10, so the diameter has a length of 10.

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Example Question #365 : Circles

True or false: A circle with radius 20 has diameter 10.

Possible Answers:

True

False

Correct answer:

False

Explanation:

The diameter of a circle is twice its radius (not the other way around), so a circle with radius 20 has diameter $2 \times 20 = 40$ .

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Example Question #364 : Circles

True or false: A circle with radius 500 centimeters has diameter one meter.

Possible Answers:

True

False

Correct answer:

False

Explanation:

The diameter of a circle is twice that of the radius, so the diameter of a circle with radius 500 centimeters is $500 \textrm{ cm} \times 2 = 1,000 \textrm{ cm}$ . However, one meter is equal to 100 centimeters, so the statement is false.

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Basic Geometry : Circles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #361 : Circles

Example Question #362 : Circles

Example Question #361 : Circles

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

Example Question #361 : Circles

Example Question #362 : Circles

Example Question #61 : Diameter

Example Question #62 : Diameter

Example Question #365 : Circles

Example Question #364 : Circles

All Basic Geometry Resources

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