The Organic Chemistry Tutor
This calculus video tutorial explains how to solve related rates problems using derivatives. It shows you how to calculate the rate of change with respect to radius, height, surface area, or volume of a sphere, circle, cone, etc. This video contains plenty of examples and practice problems such as the inverted conical tank problem, the ladder angle problem, similar triangle shadow problem, problems with circles, spheres, cubes, cones, squares, and triangles and so forth.
Here is a list of problems.
1. Finding dx/dt, dy/dt and dz/dt – Pythagorean Theorem – Right Triangle Trigonometry
2. How to find the rate of change of the distance between the origin and a moving point on the graph if the y-coordinate is increasing
3. The radius of a circle is decreasing at a rate of 4cm/min. How fast is the area and circumference changing when the radius is 8cm?
4. The surface area of a snowball at a rate of 6 square feet per hour, how fast is the diameter changing when the radius is 2 ft?
5. The side length of a square increases at a rate of 3 inches per second, how fast is the area and perimeter of the square changing when the side length is 5 in ?
6. A spherical balloon is inflated with gas at a rate of 900 cubic centimeters per minute (cm^3/min), how fast is the radius of the balloon changing?
7. The side lengths of a cube are increasing at a rate of 5 cm/s, How fast is the surface area and volume increasing?
8. A 13 foot ladder leans against a house. The ladder slides down the wall at a rate of 3 ft/min. How fast is the ladder moving away from the base of the wall when the foot of the ladder is currently 5ft from the wall? How fast is the area of the triangle changing? How fast is the angle between the ground and ladder changing?
9. Gravel is being dumped from a conveyor belt at a rate of 100 cubic feet per min (ft^3/min) forming a conical pile whose base diameter is two times the altitude. How fast is the height changing?
10. Water is leaking out of an inverted conical tank at 500 cm^3/min. The tank has a height of 24 cm and a radius of 6cm. Find the rate at which water is being poured into the tank if the water level is rising at 15cm/min.
11. A street light is mounted on a pole 24 ft tall. A man 6ft tall walks away from the pole at a rate of 4ft/s. How fast is the tip of his shadow moving when he is 20ft from the pole? How fast is the length of his shadow changing at this instant?
12. A spotlight shines on a wall 18m away. If a 2m tall man walks toward the building at a speed of 2m/s, how fast is the length of his shadow on the building changing?
13. Two cars are moving starting from the same point. One travels north and the other travels east at 30mph. At what rate is the distance between them changing?
14. At 1:00pm, ship B is 150 miles from ship A. Ship A is moving 30mph north and ship B is moving 20mph south. How fast is the distance changing at 3:00pm.
15. Airplane Problem – Travels Horizontally at an altitude of 3 miles. Radar Station Below.
16. Airplane Observer Problem – Rate of Change of Angle of Elevation – Angle Between Ground and Observer
17. Baseball Diamond Square Problem – Speed in ft/s. At what rate is the distance between first base, home plate and second base changing when he is halfway
18. Water trough problem
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THANK YOU!!!!!!
Hello a cordial greeting from the south of Colombia, would you be so kind as to upload a video about limits to infinity? using the Euler number.
I would like to delve a little more into this type of limits, thank you and I value your work and continue your work.
Dude you are a fucking wizard. I literally hope you’re getting paid handsomely for this you’re the man bro
the problem at 54:00 why did we need to find a new "r" value or quote on quote "replace r with h" when the radius was already given at 6cm i don't understand.
You draw pictures Like I do! XD
my nigga
It's been a minute since I learned these early calculus concepts and it feels so good to understand this concept so easily now since it was a confusing nightmare when I first learned it lol.
As always, OCT deserves a Nobel Prize for the number of stem graduates he's produced since he started this channel.
16: 05 so as you can see the numbers make sense ٫٫ lol 😅
This hard? Boy try u substitution!
this guy is fuckn good… love this dudes maths
My hero!!!!!❤❤❤
50:31 4:22 marking that for later
At 20:39 isn’t the dx/dt= +3
you made it way easier than it looks, thanks!
51:13
This section proved more difficult than anything else I had done up to this point in math. Really struggled with the concepts. But after about a week of obsessive studying and watching this video at least 3 times it is actually easy for me now! It’s crazy how once something clicks and makes sense it seems so simple that you wonder how you didn’t understand it from the beginning. Thanks as always for your content.
You are a life saver, the way you put helps me formulate what i need to do and then its just algebra with derivatives. This is gonna save me on my AP calc test tomorrow
Thank you so much. You really helped me a lot! 🙂
if pi is a constant why isnt it 0
1:22:14
Isn't the length of x at 1:02:57 supposed to be 20ft?
My final is tomorrow 😰
watching these videos really help me review a lot! I found out that reviewing online with videos, then checking if I did it right or wrong is the best way for me to learn. Thanks again
9:11
Minus 1, that's 3. QUICK MATHS.
Derivitive of a constant is 0. why are we keeping pi just the way it is without differentiation
42:18 what happened to dx/dt when you differentiated x/l??
Major final tomorrow, crying bittersweet tears… Wish I'd found this earlier
bruh you are a life saver
Undergraduate math student here. When I was taking AP Calculus AB back in high school this was the hardest topic that I encountered in the whole course.
omg thank you so much for this, i can literally pass my exam tomorrow for sure
22:00 how it is 12 and not 30?? (dA/dt)
still the best prof than any actual profs
is it okay to use, for example, P' instead of dp/dt? For faster solving
1:16:08 two cars are moving starting at the same point
58:17 shadow problem
This is a blessing from god
My cal final is literally tomorrow. ❤️ this video saves my life
this guy makes me feel bad at being an idiot lmao
the hardest part is finding out what you need to find and forming the functions
Your birth has brought something special