I entered 17.01 for problem 3 but it was marked wrong . Why?

If you look closely at question 3, it states to round the answer to the nearest integer. An integer is a whole number. Therefore, 17.01 is not a whole number. 17 is the nearest whole number (integer) You had the solution correct, however did not follow the directions to round to the nearest integer

Just to clarify for everybody if you press alt and then the letter P the pi symbol will pop up.

It did not work on my keyboard, I put in pi and it changed to the symbol or ALT 227 on the number pad on the side with numlock on.

How does this all work? I read all the solutions, but I still don't understand... Could someone please explain?

Lets go through the first problem. We are trying to figure out the length of arc DC. Lets find the circumference first. Circumference= 2pi*r which is also equal to diameter*pi. Therefore the circumference of the circle is 16pi. The arc measure is equal to the central angle that intercepts it. Since line CA is a diameter, it is equal to 180 degrees, so if you add the measures of angles DPA and DPC, it will equal 180 degrees. Since the measure of DPA is 60 degrees, DPC is equal to 120 degrees. Now we set up a proportion to find the part of circumference intercepted by that angle, so Arc length/Circumference = Arc measure/Degrees in a circle. Arc length/16pi = 120/360. We can simplify the fraction to the right and it will be Arc length/16pi = 1/3. Since we need to isolate the arc length, we can multiply both sides by 16pi. After that we get Arc length = 16pi/3. The length of arc DC is equal to 16pi/3. Lets also go through problem 3. We know that arc AC is equal to 152 degrees. We also know that the other two arcs, AB and BC are congruent to each other. Therefore do 360-152/2. That will be the central angle of BPC, which is 104 degrees. The equation for the arc length is this: Central angle/360 = Arc length/ Circumference. Since the radius is four the circumference will be eight. The equation is 104 / 360 = s/8pi. Multiply both sides by 8 pi since we need to isolate s, and you should end up with the answer which is 104*8pi / 360 = s. Hope this helps!

When I tried to answer problem 2, there was no pi button.

Type in pi and it will convert this to the symbol

how do you enter "pi" in your answer? i wonder where's the key located on the keyboard?

In Khan, you can often type in the word pi and the program changes it to the symbol π. You could also hold down the ALT key and type 227 on the numberpad (numberlock on) on the right side of the keyboard to get π

I find it funny that on the third question that if you put 5.41666666pi its marked wrong but it you type 5.416666666pi its correct. why does it accept that answer? but heaven forbid I put in 5.416

More than likely, it is based on what the program understands as a repeating decimal. Adding the extra 6 might be recognized as a repeating decimal, but without it, it is just a truncated number. This is common on a lot of calculators.

360-152=108 not 104 a small mistake ?

Hey.. we get 208. After this we divide it by 2 to obtain the angle. Hence, we get the angle as 104 deg

Main content

Course: High school geometry > Unit 8

Lesson 3: Arc length (from degrees)

Challenge problems: Arc length 1

Google Classroom

Solve four challenging problems that ask you to find arc length without directly giving you the arc measure.

Problem 1

In the figure below,

\overset{―}{D B}

and

\overset{―}{A C}

are diameters of circle

P

. The length of

\overset{―}{P B}

8

units.

What is the length of $\overset{⌢}{D C}$ ‍?

We are trying to figure out the length of the part of the circumference of circle

P

that begins at point

D

and ends at point

C

Let's calculate the full circumference first, then solve proportionally for the arc length based on the degrees in the arc measure.

We know that circle

P

has a radius of

8

units because

\overset{―}{P B}

is a radius.

$\begin{aligned} Circumference & = 2 π r \\ = 2 π (8) \\ = 16 π \end{aligned}$ ‍

The arc measure is equal to the measure of the central angle that intercepts the arc.

Because

\overset{―}{C A}

is a diameter,

∠ C P D

and

∠ D P A

are supplementary.

$m ∠ C P D + 60^{\circ} = 180^{\circ}$ ‍

The arc measure of

\overset{⌢}{D C}

120^{\circ}

Finally, we can set up a proportion to solve for the part of the circumference intercepted by that angle.

$\begin{aligned} \frac{arc length}{circumference} & = \frac{arc measure}{degrees in a circle} \\ \frac{arc length}{16 π} & = \frac{120^{\circ}}{360^{\circ}} \\ arc length & = \frac{120^{\circ}}{360^{\circ}} \cdot 16 π \\ = \frac{16}{3} π \end{aligned}$ ‍

The length of

\overset{⌢}{D C}

\frac{16}{3} π

Problem 2

In the figure below, the radius of circle

P

6

units.

What is the length of $\overset{⌢}{A B C}$ ‍?
Either enter an exact answer in terms of $π$ ‍ or use $3.14$ ‍ for $π$ ‍ and enter your answer as a decimal.

We are trying to figure out the length of the part of the circumference of circle

P

that begins at point

A

, passes through point

B

, and ends at point

C

Let's calculate the full circumference first, then solve proportionally for the arc length based on the degrees in the arc measure.

We know that circle

P

has a radius of

6

units because

\overset{―}{C P}

is a radius.

$\begin{aligned} Circumference & = 2 π r \\ = 2 π (6) \\ = 12 π \end{aligned}$ ‍

The measure of an arc is equal to the measure of the central angle that intercepts it.

The measures of

\overset{⌢}{A B}

and

\overset{⌢}{B C}

add up to the measure of

\overset{⌢}{A B C}

$111^{\circ} + 129^{\circ} = 240^{\circ}$ ‍

Finally, we can set up a proportion to solve for the part of the circumference intercepted by that angle.

$\begin{aligned} \frac{arc length}{circumference} & = \frac{arc measure}{degrees in a circle} \\ \frac{arc length}{12 π} & = \frac{240^{\circ}}{360^{\circ}} \\ arc length & = \frac{240^{\circ}}{360^{\circ}} \cdot 12 π \\ = 8 π \end{aligned}$ ‍

The length of

\overset{⌢}{A B C}

8 π

Problem 3

In the figure below,

\overset{―}{B C}

is a diameter of circle

P

. The length of

\overset{―}{B P}

3

units.

What is the length of $\overset{⌢}{A C D}$ ‍?
Either enter an exact answer in terms of $π$ ‍ or enter your answer as a decimal rounded to the nearest integer.

We are trying to figure out the length of the part of the circumference of circle

P

that begins at point

A

, passes through point

C

, and ends at point

D

Let's calculate the full circumference first, then solve proportionally for the arc length based on the degrees in the arc measure.

We know that circle

P

has a radius of

3

units because

\overset{―}{B P}

is a radius.

$\begin{aligned} Circumference & = 2 π r \\ = 2 π (3) \\ = 6 π \end{aligned}$ ‍

From the diagram, we see we need all of the circle except for the

35^{\circ}

arc.

$360^{\circ} - 35^{\circ} = 325^{\circ}$ ‍

The measure of

\overset{⌢}{A C D}

325^{\circ}

Finally, we can set up a proportion to solve for the part of the circumference intercepted by that angle.

$\begin{aligned} \frac{arc length}{circumference} & = \frac{arc measure}{degrees in a circle} \\ \frac{arc length}{6 π} & = \frac{325^{\circ}}{360^{\circ}} \\ arc length & = \frac{325^{\circ}}{360^{\circ}} \cdot 6 π \\ = \frac{65}{12} π \end{aligned}$ ‍

The length of

\overset{⌢}{A C D}

\frac{65}{12} π

Problem 4

In the figure below,

∠ A P B ≅ ∠ B P C

. The length of

\overset{―}{P B}

4

units.

What is the length of $\overset{⌢}{B C}$ ‍ on circle $P$ ‍?
Either enter an exact answer in terms of $π$ ‍ or use $3.14$ ‍ for $π$ ‍ and enter your answer as a decimal rounded to the nearest hundredth.

We are trying to figure out the length of the part of the circumference of circle

P

that begins at point

B

and ends at point

C

Let's calculate the full circumference first, then solve proportionally for the arc length based on the degrees in the arc measure.

We know that circle

P

has a radius of

4

units because

\overset{―}{P B}

is a radius.

$\begin{aligned} Circumference & = 2 π r \\ = 2 π (4) \\ = 8 π \end{aligned}$ ‍

The arc measure is equal to the measure of the central angle that intercepts the arc.

The sum of the central angles in any circle is

360^{\circ}

. We know

∠ A P B

and

∠ B P C

are congruent.

$\begin{array}{r} m ∠ A P B + m ∠ B P C + 152^{\circ} = 360^{\circ} \\ 2 (m ∠ B P C) + 152^{\circ} = 360^{\circ} \\ m ∠ B P C = 104^{\circ} \end{array}$ ‍

The measure of

∠ B P C

104^{\circ}

. Likewise, the arc measure of

\overset{⌢}{B C}

104^{\circ}

Finally, we can set up a proportion to solve for the part of the circumference intercepted by that angle.

$\begin{aligned} \frac{arc length}{circumference} & = \frac{arc measure}{degrees in a circle} \\ \frac{arc length}{8 π} & = \frac{104^{\circ}}{360^{\circ}} \\ arc length & = \frac{104^{\circ}}{360^{\circ}} \cdot 8 π \\ = \frac{104}{45} π \end{aligned}$ ‍

The length of

\overset{⌢}{B C}

\frac{104}{45} π

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fpgailliot
Posted 8 years ago. Direct link to fpgailliot's post “I entered 17.01 for probl...”
I entered 17.01 for problem 3 but it was marked wrong . Why?
Button navigates to signup pageComment on fpgailliot's post “I entered 17.01 for probl...”
(42 votes)
Answer
- Ron Lakerveld
  Posted 7 years ago. Direct link to Ron Lakerveld's post “If you look closely at qu...”
  If you look closely at question 3, it states to round the answer to the nearest integer. An integer is a whole number. Therefore, 17.01 is not a whole number. 17 is the nearest whole number (integer) You had the solution correct, however did not follow the directions to round to the nearest integer
  Comment on Ron Lakerveld's post “If you look closely at qu...”
  (50 votes)
Kyra Gilbert
Posted 8 years ago. Direct link to Kyra Gilbert's post “How does this all work? I...”
How does this all work? I read all the solutions, but I still don't understand... Could someone please explain?
Button navigates to signup pageButton navigates to signup page
(12 votes)
Answer
- Aryan
  Posted 8 years ago. Direct link to Aryan's post “Lets go through the first...”
  Lets go through the first problem. We are trying to figure out the length of arc DC. Lets find the circumference first. Circumference= 2pi*r which is also equal to diameter*pi. Therefore the circumference of the circle is 16pi. The arc measure is equal to the central angle that intercepts it. Since line CA is a diameter, it is equal to 180 degrees, so if you add the measures of angles DPA and DPC, it will equal 180 degrees. Since the measure of DPA is 60 degrees, DPC is equal to 120 degrees. Now we set up a proportion to find the part of circumference intercepted by that angle, so Arc length/Circumference = Arc measure/Degrees in a circle. Arc length/16pi = 120/360. We can simplify the fraction to the right and it will be Arc length/16pi = 1/3. Since we need to isolate the arc length, we can multiply both sides by 16pi. After that we get Arc length = 16pi/3. The length of arc DC is equal to 16pi/3.
  Lets also go through problem 3. We know that arc AC is equal to 152 degrees. We also know that the other two arcs, AB and BC are congruent to each other. Therefore do 360-152/2. That will be the central angle of BPC, which is 104 degrees. The equation for the arc length is this: Central angle/360 = Arc length/ Circumference. Since the radius is four the circumference will be eight. The equation is 104 / 360 = s/8pi. Multiply both sides by 8 pi since we need to isolate s, and you should end up with the answer which is 104*8pi / 360 = s.
  Hope this helps!
  Button navigates to signup page
  (48 votes)
Zane Oliver Watt Hoven
Posted 4 years ago. Direct link to Zane Oliver Watt Hoven's post “Just to clarify for every...”
Just to clarify for everybody if you press alt and then the letter P the pi symbol will pop up.
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(17 votes)
Answer
- David Severin
  Posted 4 years ago. Direct link to David Severin's post “It did not work on my key...”
  It did not work on my keyboard, I put in pi and it changed to the symbol or ALT 227 on the number pad on the side with numlock on.
  Comment on David Severin's post “It did not work on my key...”
  (10 votes)
alysahbland
Posted 8 years ago. Direct link to alysahbland's post “For number four, I answer...”
For number four, I answered with 104/45 times 3.14 and it was marked wrong. Then I checked my answer and the only difference between the answer provided and mine is that they have the pi sign instead of 3.14. I don't think it is fair to mark an answer wrong if you don't provide the sign in the drop down box. I was just wondering if I was wrong?
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(10 votes)
Answer
- Ashu
  Posted 8 years ago. Direct link to Ashu's post “Writing pi instead of jus...”
  Writing pi instead of just 3.14 is correct, because even though the pi sign isn't provided, you just spell out pi rather than 3.14, because pi means 3.1415926...., while just 3.14 is incorrect.
  Comment on Ashu's post “Writing pi instead of jus...”
  (1 vote)
Jedidah440
Posted 3 years ago. Direct link to Jedidah440's post “how do you enter "pi" in ...”
how do you enter "pi" in your answer? i wonder where's the key located on the keyboard?
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(2 votes)
Answer
- David Severin
  Posted 3 years ago. Direct link to David Severin's post “In Khan, you can often ty...”
  In Khan, you can often type in the word pi and the program changes it to the symbol π. You could also hold down the ALT key and type 227 on the numberpad (numberlock on) on the right side of the keyboard to get π
  Button navigates to signup page
  (13 votes)
Kasim Ahmed
Posted 5 years ago. Direct link to Kasim Ahmed's post “With some of these questi...”
With some of these questions, there is no option to use the 'pi' symbol.
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(6 votes)
Answer
- Johnpaul
  Posted 5 years ago. Direct link to Johnpaul's post “It’s because you have to ...”
  It’s because you have to round or use 3.14 instead of pi.
  Comment on Johnpaul's post “It’s because you have to ...”
  (0 votes)
kiera.taylor
Posted 4 years ago. Direct link to kiera.taylor's post “When I tried to answer pr...”
When I tried to answer problem 2, there was no pi button.
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(3 votes)
Answer
- David Severin
  Posted 4 years ago. Direct link to David Severin's post “Type in pi and it will co...”
  Type in pi and it will convert this to the symbol
  Button navigates to signup page
  (5 votes)
berhanu seyoum
Posted 6 years ago. Direct link to berhanu seyoum's post “360-152=108 not 104 a sm...”
360-152=108 not 104 a small mistake ?
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(0 votes)
Answer
- B. Akshay Narayanan
  Posted 4 years ago. Direct link to B. Akshay Narayanan's post “Hey.. we get 208. After t...”
  Hey.. we get 208. After this we divide it by 2 to obtain the angle. Hence, we get the angle as 104 deg
  Button navigates to signup page
  (3 votes)
breyonajglenn
Posted 4 years ago. Direct link to breyonajglenn's post “none of this makes sense!”
none of this makes sense!
Button navigates to signup pageComment on breyonajglenn's post “none of this makes sense!”
(4 votes)
Answer
J H
Posted 2 years ago. Direct link to J H's post “I find it funny that on t...”
I find it funny that on the third question that if you put 5.41666666pi its marked wrong but it you type 5.416666666pi its correct.
why does it accept that answer? but heaven forbid I put in 5.416
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- David Severin
  Posted 2 years ago. Direct link to David Severin's post “More than likely, it is b...”
  More than likely, it is based on what the program understands as a repeating decimal. Adding the extra 6 might be recognized as a repeating decimal, but without it, it is just a truncated number. This is common on a lot of calculators.
  Button navigates to signup page
  (4 votes)