Arc Distance Math Riddle | Math SAT & ACT Prep | JusticeTheTutor #shorts

[colinthompson]

Ah yes the average 18 meter diameter house clock that every household has on their wall

[kididychannel]

This video is about how to make math harder than it really is.

My solution was:
3hours is 1/4 of 12 hours and the radius of the circle is 9, the formula for finding the circumference of a circle is 2πr, so the answer is (1/4)*2r*π or 4.5π.

[accanino]

Just find the circumference and divide by 4. Easier than converting to arc length and remembering how radians work.

[larrywest]

Ooops: 4.5π is not a distance - forgot the units (meters).

[dunanub]

Also: The length(radius) isn't given, only the radius of the clock itself is. Now in my experience the average hour hand is significantly shorter than the clock radius, needing to fit inside the clock etc...

[TheoWerewolf]

A slightly easier way to visualise this.
The circumference of a circle is c = 2πr.
One time around the clock (ie: the circumference) is 12 hours. so fraction of circumference f = 3hr/12hr = 1/4.
So angular distance ang = c * f
ang = 2πr * 1/4 or πr/2
r=9
ang = 9π/2 or 4.5π
A.

[n]

I am a big proponent of using logic instead of trying to remember the “formula for the distance of an arc.”

We know at least one formula relating to a circle, very very well. The circumference is 2•pi•r. We know that in 3 hours, the hours hand of the clock travels 3/12 of the circumference of the clock.

Therefore 3/12 •2•pi•r = 6/12 * pi * 9 = 4.5pi

[alex]

I mean most of us know that the circumference of a circle is pi times the diameter, so it’s just 1/4 of 18 pi, which is a more straightforward solution most people would follow a lot easier

[missy]

I always love option D in these questions! hehe

[Sky-pgxy]

For anyone that has trouble remembering that formula (Radians) are literally the number of “radiuses”, or the grammatically correct (radii) you’ve traveled around the circle. If you want the linear distance (arc distance), just multiply by how long each radius is.

[cleung]

Actually, the hour hand of clock is shorter than the radius of the clock. The arc length traveled by hour hand should be smaller than 4.5π.

[aafarookh]

You are so good at explaining…plz cover the rest of topics of maths also…bless you sir 😊

[DuckInGameStop]

I just calculated the circumference of the circle and divided it by 4, it's 18π and divided by 4 I got 4.5π

[blackpinkinyourarea]

I would've just answered "lol what"

[azgrxy]

I’m enjoying these math videos way more than I’m supposed to lol

[atdynax]

I got it with a different formula. The circumference of a circle is 2*Pi*r. R=9 makes 2*9*Pi. 18Pi must be divided by 4 and you get 4, 5Pi

[Savannah-]

Oh my gosh! I love radians and unit circle stuff. We just finished our unit on unit circle.

[DD-ngbj]

I really appreciate your postings. Keeps my mind sharp ❤ You do an excellent job with the explanations… great teaching skills!

[mmk]

I love to do these in my head by pausing it and then u pausing to see if I got it right!!! Thank

[tunistick]

"this one would be very funny"
Yea the fact that radius of an hour hand is *9 METERS!!*