A cell tower can service 75 sq miles. How far away from the tower can you be and still connect?

Geometry word problem area of circle.
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[@radioboyintj]

You can't connect. The tower is owned by Comcast Xfinity And they no longer offer one free hour of wifi per month to non-comcast subscribers

[@joannkania1762]

That sounds like the smart ass answers I write in organic chemistry when Babbler would ask for those weird compounding steps and I fhad no idea what to do😅

[@vincentrobinette1507]

That's why you need AT&T.

[@bobcarn]

I came up with about 4.88 miles. Area of a circle is Pi times Radius squared. So 75 = 3.1416 * R * R. R is Radius, which is the distance from the center of the circle (yeah, I started thinking of a square for a second before I pictured it in my mind). Doing all the algebra stuff left me with 4.88. .... YAY!

[@danmc7815]

Watching now, but my answer before I hit play was the same. 75=pi r-squared. Solved for r.

[@billcravens3478]

Bingo!

[@simonharris4873]

4.89, if you want full marks.

[@DavidRobinson-rj2sp]

4.88 miles as the coverage is circular (discount negative solution). Use formula for area of a circle transposed to give radius.

[@m.h.6470]

close, but you have a rounding error of 0.01, as the correct result is 4.8860..., which should be rounded to 4.89

[@DavidRobinson-rj2sp]

@@m.h.6470: The number of decimal places was not specified so no need to round up.

[@m.h.6470]

@@DavidRobinson-rj2sp Sure, but 4.88 is still wrong. You can't just cut after 2 digits... that is called rounding down.

[@DeltaMikeTorrevieja]

Just under 5 miles, no calculator, etc. Just divide by 3 (and a bit, if you must), gives 25 (or a bit less) and square root.

[@genzu6388]

My thoughts exactly! No need for a 15 minute video, 10 mins tops to explain to people who genuinely don't know about the radius and pi and pi*r^2 calculation.

[@silverhammer7779]

The problem should state, "assume a circular radiation pattern for the antennas." Some cellular antennas are designed to have directional patterns to favor certain service areas.

[@limogesfarmer6326]

It's a math / geometry problem... :D

[@glenwardgross366]

John great problem. Most ppl do not understand how towers work. Most people would think you can be 75 miles from the tower and get signal. Might I suggest a cell phone triangleulation problem. Demenstrating how you can be tracked on your phone. JAT

[@laurendoe168]

The answer depends HEAVILY on the type of antenna. I presume it is an omnidirectional antenna rather than a directional one. A directional antenna basically has a "cone" of service that allows for significantly farther distances, at the cost of significantly less coverage outside of the cone.

[@DavidRobinson-rj2sp]

The clue is in the question - the area covered so it is the radius from the cell tower on a flat plane on the x-axis.

[@festidious2644]

@@DavidRobinson-rj2sp Isn't the x-axis one dimension? Doesn't it have to be x-y for two dimensions? Boy, these seemingly simple things get me confused.

[@m.h.6470]

@@festidious2644 you are correct. though it obviously depends on how you define x, y and z axis. The typical way is the z axis to be the plumb line (meaning it points to the center of the earth) and the x and y axis to be orthogonally to z and to each other. With this, the x-y-plane would be roughly the ground or parallel to the ground.

[@laurendoe168]

@@DavidRobinson-rj2sp Providing the area covered does not imply the type of antenna used. If it's a directional antenna, the area covered is the sector of a circle. This is determined by (1/2) * (theta * r^2) where theta is in radians. The more directional the antenna is, the smaller the theta and the narrower the beam. As a result, the farther the distance from the antenna can be. FYI - If it's omnidirectional, the formula is still (1/2) * (theta * r^2), it's just that theta = 2 * pi, which when combined with the (1/2) leaves just pi... which is then multiplied by r^2

[@kennethwright870]

75= pi*r^2, so R= sqrt(75/pi)mi, so R=approx 4.89 mi

[@violinkev1]

I'll bet I could be a foot away from the tower and still connect.

[@vincentrobinette1507]

True, because you're within the 75 square mile service AREA of the tower, within the 4.88 mile service RADIUS.

[@GaryBricaultLive]

For those of us who understand the engineering considerations, the problem needs to be fully specified. Assuming the tower will radiate in a circular pattern and the tower height nor the terrain affects the radiated energy, it is a simple Distance = (A / Pi)^1/2 problem.

[@heatherhiggins2002]

Trick question, they're is no cell phone tower that has a 75 sq mi reach. For seemless travel in a flat area (no hills/mountains) you need a tower every 3-7 miles. Everytime the distance from the tower doubles the strength/intensity of the signal square routes. So my answer is 7 miles max for data and possibly 20 miles max for a phone call.( and thats on a clear day/flat area/high strength tower).

[@RoderickEtheria]

75=pi×r^2 sqrt(75/pi)=r Slightly less than 5 miles. This assumes no dead zones within area, which if there are any, it extends the range the tower might be able to reach.

[@jerry2357]

In reality, the coverage heavily depends on the terrain, and people on the top of a hill many miles away could get a signal when people nearer to the tower could not. I've heard of people on the south coast of England getting charged roaming fees because the best signal that they could receive was from France.

[@bluejedi723]

In my area depending on where you are one of 3 things: Great coverage. Roaming charges because best signal is 200 miles away OR stand on your roof and recite hail mary prayer perfectly in 5 languages 3 times and promise to be a real good boy and maybe you might get a minute of service.

[@ls1powered240sx]

Depends on environment.. identical towers one in Miami humid and heavy populated you might get a half mile. In the desert of Nevada i have seen devices hashing to towers at more that 50 miles. Seasonal foliage is big at decreasing range as the moisture in the leaves suck up all the signals.

[@Client915]

So many people commenting, and only a few accurate answers; 4.89. Why so many people struggling with rounding? 4.887 rounds to 4.89, not 4.88. I guess if this were a riddle or a tick question then your could say that rounding up would put you outside the "cell service area", but it appears the intent of these videos are about the math and not about the semantics of the question. At least they threw a "±” in the video for some reasonable doubt to answer given.

[@johnchud7507]

Why is everyone thinking in circles when cell towers have 4 antenna's, on for each compass point, and working the industry tells me 8.6 miles, this due to vast amount of power being pushed out

[@mytube082007]

Mental math yielded this: Pi x r^2 = 75 r = sqrt (75/3.14) = 5 x sqrt (3)/sqrt (3.14) = approx. less than 5

[@Colorado_Native]

I calculated the tower height at about 13 feet tall. If you disregard the reflectivity, etc, you take the 75 feet and the square root is 8.66. Now assume the tower transmits in a roughly circular pattern so you divide the 8.66 by 2 because it's essentially transmitting equally all around giving you 4.33 miles of transmission. Now, if you have an unrestricted view, let's say at a beach, and you are 6 feet tall standing on a 7 foot high wall, that gives you a height of 13 feet. Take the 13 feet X 1.5 giving you 19.5 and the square root of that is 4.41 miles you can see (or transmit) unobstructed in one direction. So the tower is about 13.5 feet tall. We used to have to figure out how far our U-2 aircraft could 'see' when taking photos.I tried typing in using my tablet keyboard but couldn't. Basically, take the height you are observing from (let's say your eyes are 100 feet up) times 1.5 then take the square root of that number. So, 100 X1.5= 150 and the square root of that is 12.25 miles. If you are in a high-flying airplane, let's say 70,000 feet; it would be 70,000 X 1.5 = 105,000.The square root of 105,000 is 324. So you can see 324 miles away at that altitude. Of course the higher you are the greater the error is going to be. Thanks for posting this question.

[@tomtke7351]

do we assume circular coverage

[@vincentrobinette1507]

That was my guess, and I had to watch the video to see if I got it right. Since the story didn't define a cardioid pattern, I could only assume that it was an omnidirectional radiating antenna. I guessed right.

[@stuartofblyth]

I correctly solved the prom. Here in the UK we would call it a "problem".

[@frowe327]

😊😊

[@frederickdvorak6502]

1) The question is badly formulated (again ...). You could be anywhere within the perimeter defined by the radius of that circle, if the signal is curcular. In theory, there's an infinite number of solutions within the limits of that circle. The correct question should include the maximum distance in miles to the tower to still be able to connect to its circular signal; show your result rounded to the 2nd decimal place. 2) 15 minutes to answer that question is pushing it by at least 10 minutes, advertising included.

[@devonwilson5776]

Greetings. I am not sure why I erroneously stated that the answer to the question asked should be 4.89 square miles in my previous response. I trust that viewers will have read the response and therefrom deduce that it is an error for the reason that it is explicitly stated that we were determining the radius. Radius is determined in units and not square units. Honest mistake. Late night fatigue.

[@SteveSearle]

When a reply concerning an error is so elequently stated 😊

[@devonwilson5776]

@@SteveSearle Greetings. Much blessings.

[@brdavis]

I just kept thinking of Mr. Popo from Dragon Ball Z abridged saying "All these squares make a circle" while doing the calculation.😂

[@bobfisher8547]

The 75 mi^2 premise is not correct. The primary scientific limitation is the height of the cell tower and the height of the receiver (assumed to be about 3 ft) and the curvature of the earth blockage. In West Texas oilfield sites routinely depend on cellular service to sometimes ~30 miles. The practical limitation is the cellular carriers intentionally monitor the users' GPS to determine the distance and shut off service beyond a set distance (I've seen 20 miles used) to prevent far distant cellphones and modems and cellphones on aircraft from connecting because they use channel re-use for second and third adjacent cell sites and the distant cellphones create interference with the re-use plans (the "cell" part of cellular)

[@bobcornwell403]

I came up with approximately 4.89 miles in significant figures.

[@vincentrobinette1507]

I was able to solve it EXACTLY the way shown in this video. r= the square root of the area / Pi. (radius being the effective distance from the tower, in the middle of the circle)

[@jonathanteegardin9242]

Depends. Is the service circular it triangular?

[@festidious2644]

Wholly cow, John: I can't believe you got the same answer as I did. I figured you would go with some weird square with the tower in the middle and then how far to the corners. Good going!

[@wimharter]

When a term moves from one side of the equals sign to the other it changes it's sign. Adding an extra step of dividing both sides by π is unnessecry.

[@BavonWW]

Does the answer have to include the amount of hops the frog will require to get to the edge?

[@harlie-mae1557]

15 miles on full data rate, 25 miles on half data rate as used in Australia.

[@homeauburnRaja-hm3gq]

Approximately 75/3=5. It can be between 4.5 and 5.25 miles. Signal reduces gradually.

[@harpleblues]

Depends on the directionality and polarization of the antenna.

[@OsmaroAcosta]

Does it also depend on the frequency and the modulation?

[@devonwilson5776]

Greetings. Fortunately for me I did courses in audio video repairs and maintenance. Accordingly, it is my understanding from the details given that the Tower is transmitting radio signals to cover a circular area of 75 square miles. Therefore, the Tower would be situated, located, in the center and we are required to determine the radius of that circle. Using A= Pi ×R^2, we have 75=22/7×R^2, and R^2=(75×7)/22 square miles = 525/22 square miles =23.8636, and R=23.8636^1/2 square miles =4.89 square miles. The answer is 4.9 square miles, rounded.

[@BavonWW]

I concur; 🙃

[@devonwilson5776]

@@BavonWW Greetings. Blessings.

[@gregcornelsen6644]

Except distance is measured linear not in square anything. So 4.9 miles not square miles😊

[@devonwilson5776]

@@gregcornelsen6644 Greetings. Thanks. The error was discovered and corrected immediately after posting in another post. I like the fact that you have noticed the error and pointed it out for others to learn. Personally, I did not learn anything. It was just an error on my part, perhaps resulting from late night fatigue. Blessings.

[@johntarun9177]

Some depends on line of sight.

[@russelllomando8460]

got it. thanks

[@freedomfighter313]

It depends on a lot of things. Sometimes the "reception area" does not adhere to the exact mathematical calculations....ie you just don't get the reception as promised (calculated). So in this case the circumference area based the calculated radius might not work....I could be wrong......but (75 x 1) is also 75 sq. miles.....🤷🤷🤨🤨

[@rodfulford4306]

Square root of 75/pi

[@olufunkealabi8612]

Addendum to the question should have ended with, assuming 75sq miles circle area. Then you use tge appropriate formuka

[@ldewproductions7271]

About 10seconds to come up with just under 4.9 miles. 75 divide by 3=25, square root is 5 so as bit less. Near enough

[@frowe327]

You're right about the time, because, although the radio signals travel at the speed of light it DOES take your phone about 10 seconds to come up when you turn it on! 😂 And of course just under 5 miles is the right range also!😂

[@richardl6751]

At 4:20 The term is "omnidirectional".

[@limogesfarmer6326]

At 4:20, eh? I think I'll smoke a doobie and watch that part again... :D

[@richardl6751]

@@limogesfarmer6326 Oh far out man. You could sit on a bar stool, then spin and get an omnidirectional view of the World.

[@bluejedi723]

In my area (with poor coverage) the correct answer is you need to stand on your roof recite hail mary perfectly in 5 languages 3 times promise to be a real good boy and maybe you might get a minute of service.

[@billcravens3478]

About 4.8+ miles. Did it in my head, no paper or calculator, so "close" but not exact.

[@mrsteveinsandiego]

I hafta remember how to figure the square root from algebra/trig, i guess. At 75 yrs old, ive comPLETEly 4gotten.

[@raynewport9395]

How tall is the tower?

[@simonharris4873]

4.88 Miles? They must round differently in the UK. Where I come from, 4.886 would round to 4.89.

[@slshusker]

Raise your hand if you first started calculating in your heand with a square and then realized it was a circle.

[@donatist59]

Way more complicated than I thought it would be. Math just demoralizes me.

[@peterthompson9854]

Well that took 3 seconds to work out!

[@CR3W1SH03S]

Pi x r^2 = A so sqrt (75 / pi) = 4.88 mi.

[@stevedietrich8936]

roughly 5 miles area=pi x radius squared

[@glenwardgross366]

John what is your favorite number and why? I will tell you my two favorite numbers. So it is a two for one.

[@URNOTGJK]

4.33

[@dc1741]

That's assuming flat earth/similar topography over the area.

[@pibbles-a-plenty1105]

sq rt ( A/pi ) = r r = 4.887 mi.

[@Boshamengra]

4.8

[@fireofenergy]

You're the best! Thanks for explaining, except that 15 minutes is excruciatingly long 😏

[@gerritkr]

approx: 4.89 miles

[@glennredwine289]

4.886 miles=(75÷3.14159)^.5

[@rossivey3509]

8.67

[@KiloFeenix]

It depends on your cell phone

[@RJ-uu9mh]

What if it's 1 mile wide by 75 miles long? That's 75 square miles.

[@kennethdias9988]

Pi r squared = 75 go backwards it’s about 4.89

[@keithschipiour4684]

If it's a Verizon tower you could be standing underneath it and still not connect . Trick question does not relate to real world experiences.

[@charlesstarling1091]

4.33 miles

[@ozfire7]

4.88 miles.

[@johnfritzel9833]

Square root of 75 / 3.14

[@colleencurrier1586]

Is it 75?

[@lewisreiman8124]

4.88 miles

[@dave9456]

37.5 miles

[@fireofenergy]

Bad connection, too many users trying to figure out the math at the same time (many of you won't get the correct answer 😅

[@maredimahlomotja1896]

8.6 miles away

[@zachansen8293]

75/3=25. sqrt=5. pi is little > 3 so ans little < 5

[@travel50sb]

75 miles

[@deograciousuwiragiye8429]

9 .x miles d'imiter place to be connected.

[@OsmaroAcosta]

If it's Optus, 1KM max 😅

[@mustafaalshaikh1061]

About 8 miles

[@m.h.6470]

more than 3 miles off...

[@Kerbeygrip]

Can’t divide by pi in my head. Still took me 30s!

[@frederickdvorak6502]

My trick for a good-enough approximation: Divide by 3 and deduct 5% ... 75 / 3 = 25 ; 25 - 25*5% = 25 - 1.25 = 23.75 vs 75 / Pi = 23.87

[@pjstar2009]

I love math, but don't like the long explanations with all the words...

[@effyleven]

Can't he say "problem?"

[@geraouttahermaeens1075]

I’m dumb…..I came up with 18.66 miles……….. I did not know 4.88x4.88=75 miles squared…….the only pi I know is apple pie

[@limogesfarmer6326]

I'm not watching this for more than a couple minutes. It took me 3 seconds to come up with 4,88 miles. This is literally grade school math/geometry. Just how bad is the ecuation level in thgis guy's country? Who is the target audience, and why does it need a 15 minute video to figure out area = Pi x r squared? And why is this in a google news feed? Google must think I'm really bad at this (when this is a forte of mine.....).

[@philo5923]

Your video could’ve lasted two minutes. It seems like you really like to hear yourself talk. Math is not philosophy. You could solve this easy problem much quicker and more to the point.

[@lukeknowles5700]

John, your attention to detail in language does not match your attention to detail in math. Instead of fully pronouncing the word "problem", you tend to take shortcuts, saying either "promm" or "prollem". Please remember that accuracy in language is every bit as important as in the sciences. I enjoy your channel, and even though I'm an old fart, your problems keep me sharp.

[@mrboxcar100]

8.66

[@darellpiper7227]

4.33 miles

[@chamberlainarmand]

37.5 miles