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Example Questions

Example Question #1131 : Ged Math

Use 3.14 for pi and round your answer to the nearest hundredth.

Find the area of a circle with a diameter of 12cm.

Possible Answers:

$37.68cm^{2}$

113.04cm

452.16cm

$113.04cm^{2}$

$452.16cm^{2}$

Correct answer:

$113.04cm^{2}$

Explanation:

First we need to recall that the formula for area of a circle is

$Area=r^{2}\cdot \pi$

Where is radius and $\pi$ is 3.14

The circe we are working with has a diameter of 12. The diameter is twice the length of the radius, so to find the radius we cut it in half, and we get 6cm.

Now we can plug our radius and pi into our equation and solve for the area

$Area=(6cm)^{2}\cdot3.14$

Following order of operations, first we need to address the exponent. Any number to the second power (squared) is that number times itself one time (in this case it is 6x6)

$Area=36cm^{2}\cdot3.14$

Next we multiply

$Area=113.04cm^{2}$

Since we multiplied two terms whose units are in cm, our answer is in centimeters squared.

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Example Question #161 : Circles

Find the area of a circle given that the distance from its center to its edge is 6.25 meters.

Possible Answers:

122.72m^2

39.06m^2

19.53m^2

47.65m^2

Correct answer:

122.72m^2

Explanation:

Find the area of a circle given that the distance from its center to its edge is 6.25 meters.

Area of a circle is given by:

$A=\pi r^2$

We know that our radius is 6.25 m, given that this is the distance from the center to the edge.

Plug in and solve.

$A=\pi (6.25m)^2=122.7185 m^2\approx 122.72m^2$

So our answer is

122.72m^2

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Example Question #162 : Circles

If a circle has a radius of 5, what is its area?

Possible Answers:

$A=10\pi$

$A=25\pi$

$A=5\pi$

$A=100\pi$

$A=5\pi^2$

Correct answer:

$A=25\pi$

Explanation:

Recall the formula for the area of a circle

$A=\pi r^2$

Here, r is the radius, which in this case is 5

$A=\pi (5)^2=25\pi$

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Example Question #169 : Geometry And Graphs

If the diameter of a circle is centimeters long, what is the area of the circle?

(Leave answers in $\pi$ )

Possible Answers:

$25\pi$

$\50\pi$

$100\pi$

$10\pi$

Correct answer:

$25\pi$

Explanation:

The formula to calculate the area of a circle is defined as:

$A_{circle}=\pi*r^2=\pi*(\frac{d}{2})^2$

The diameter is twice the length of the radius, or . To find the radius, we must divide the diameter by 2.

$r=\frac {10}{2}=5$

Now, we plug in into the formula to find the area of the circle:

$A_{circle}=\pi*(5)^2=\pi*25=25\pi$

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Example Question #1 : Central Angles And Arcs

Sector

Note: Figure NOT drawn to scale.

Refer to the above diagram.

The length of arc $\widehat{MN}$ is $12 \pi$ .

The length of arc $\widehat{MYN}$ is $18 \pi$ .

What is the area of the white sector?

Possible Answers:

$540 \pi$

$90 \pi$

$135 \pi$

$360 \pi$

Correct answer:

$135 \pi$

Explanation:

The circumference of the circle is the sum of the lengths of the arcs, which is

$C = 12 \pi + 18 \pi = 30 \pi$ .

The white sector has degree measure

$\frac{ 18 \pi }{ 30 \pi} \times 360 ^{\circ} = 216 ^{\circ}$ .

The radius of the circle can be found using the circumference formula, setting $C = 30 \pi$ :

$C = 2 \pi r$

$30 \pi = 2 \pi r$

$r = 30 \pi \div 2 \pi$

r = 15

The area of the white sector is therefore

$A = \frac{216}{360 } \cdot \pi r^{2} = 0.60 \cdot \pi \cdot 15^{2} = 225 \cdot 0.60 \cdot \pi = 135 \pi$ .

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Example Question #2 : Central Angles And Arcs

Sector

Note: Figure NOT drawn to scale.

Refer to the above diagram.

The area of the shaded sector is $24 \pi$ . The area of the white sector is $40 \pi$ .

What is the length of arc $\widehat{MN}$ ?

Possible Answers:

$10 \pi$

$4 \pi$

$6 \pi$

$8 \pi$

Correct answer:

$6 \pi$

Explanation:

The area of the circle is the sum of the areas of the sectors, which is

$A = 24 \pi + 40 \pi = 64 \pi$ .

The degree measure of the arc of the shaded sector is

$\frac{24 \pi}{64 \pi} \times 360 ^{\circ } = 135 ^{\circ }$ .

The radius can be found by solving for and substituting $A = 64 \pi$ in the area formula:

$A = \pi r^{2}$

$64 \pi = \pi r^{2}$

$r^{2} = 64$

r = 8

The length of arc $\widehat{MN}$ is

$\frac{135}{360} \cdot 2 \pi r = \frac{135}{360} \cdot 2 \cdot 8 \pi = 6\pi$ .

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Example Question #3 : Central Angles And Arcs

Circle

What percent of the above circle has not been shaded in?

Possible Answers:

$77\frac{7}{9 } \%$

$80 \%$

$75 \%$

$87\frac{1}{2} \%$

Correct answer:

$77\frac{7}{9 } \%$

Explanation:

There are a total of 360 degrees to a complete circle. The shaded sector has degree measure $80^{\circ }$ , so the unshaded sector has degree measure

$360 ^{\circ }- 80^{\circ }= 2 80^{\circ }$

Also, a sector of $N^{\circ }$ is $\frac{N}{360} \times 100 \%$ of the circle, so, setting N = 280 , we find that the unshaded sector is

$\frac{280}{360} \times 100 \%$

$= \frac{28,000}{360} \%$

of the circle. This reduces to

$\frac{28,000\div 40 }{360 \div 40 } \%$

$=\frac{700 }{9 } \%$

$=77\frac{7}{9 } \%$ ,

the correct percentage.

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Example Question #2 : Central Angles And Arcs

Circle

What percent of the above circle has been shaded?

Possible Answers:

$61\frac{1}{9} \%$

$66\frac{2}{3} \%$

$69\frac{4}{9} \%$

$58\frac{1}{3} \%$

Correct answer:

$61\frac{1}{9} \%$

Explanation:

There are a total of $360^{\circ }$ in a circle. The unshaded portion of the circle represents a $140^{\circ }$ sector, so the shaded portion represents a sector of measure

$360^{\circ } - 140^{\circ } = 220 ^{\circ }$ .

This sector represents

$\frac{ 220 ^{\circ }}{360^{\circ } } \times 100 \%$

$= \frac{ 22000}{360 } \%$

$= \frac{ 22000 \div 40 }{360 \div 40 } \%$

$= \frac{ 550 }{9 } \%$

$= 61\frac{1}{9} \%$

of the circle.

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Example Question #2 : Central Angles And Arcs

What percentage of a circle is covered by a sector with a central angle of $240^{\circ}$ ?

Possible Answers:

$87.5\%$

$50 \%$

$66.67 \%$

Not enough information to determine.

Correct answer:

$66.67 \%$

Explanation:

What percentage of a circle is covered by a sector with a central angle of $240^{\circ}$ ?

To find the percentage of a circle from the central angle, we need to use the following formula:

$\%=\frac{\theta}{360^{\circ}}*100$

Where theta is our central angle.

Plug in our given degree measurement and simplify.

$\%=\frac{240^{\circ}}{360^{\circ}}*100=66.67 \%$

So, our answer is 66.67%

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Example Question #3 : Central Angles And Arcs

Find the length of the minor arc if the circle has a circumference of $81\pi$ .

Possible Answers:

$3\pi$

$18\pi$

$9\pi$

$72\pi$

Correct answer:

$9\pi$

Explanation:

Recall that the length of an arc is a proportion of the circumference, just like how the measure of a central angle is a proportion of the total number of degrees in a circle.

Thus, we can write the following equation to solve for arc length.

$\text{Arc length}=\frac{\text{central angle}}{360}(\text{circumference})$

Plug in the given central angle and circumference to find the length of the minor arc .

$\text{Arc length}=\frac{40}{360}(81\pi)=9\pi$

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GED Math : GED Math

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #1131 : Ged Math

Example Question #161 : Circles

Example Question #162 : Circles

Example Question #169 : Geometry And Graphs

Example Question #1 : Central Angles And Arcs

Example Question #2 : Central Angles And Arcs

Example Question #3 : Central Angles And Arcs

Example Question #2 : Central Angles And Arcs

Example Question #2 : Central Angles And Arcs

Example Question #3 : Central Angles And Arcs

All GED Math Resources

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