Question

gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. it forms a pile in the shape of right circular cone whose base diameter and height are alwasy the same. how fast is the height of the pile increasing when the pile is 13 feet high?

Answer 1

do you know the expression for the volume of a cone?

Answer 2

the volume of a right circular cone with height h and the radius of the base r is given by V=(1/3)(pi)(r^2)(h)

Answer 3

i dont what that means?

Answer 4

" circular cone whose base diameter and height are alwasy the same"
V=(1/3)(pi)(r^2)(h) d= 2r = h -> r = h/2

Answer 5

V= (π/3) ( h/2 ) ²h
Now simplify and find V' :)

Answer 6

thanks :)

Answer 7

waitt.....how do you find V' ?

Answer 8

yeah but should i solve for V casue then its just a number and if i take the derivative of a number its 0...or do i not plug 13 in for h and take the derivative of (pi/3)(h/2)^2 h??

Answer 9

okay but idk how to find the derivative of that :(

Answer 10

okay i think im confused becasue i dont know how to simplify (pi/3)(h/2)^2(h)..like do you want me simplify that then take the derivative of that then plug the numbers in?

Answer 11

okayy im sorry but i dont know how to simplify that like its letters i mean i guess you could make it (pi/3)(h/2)(h/2)(h) but i dont know what else i can do to simplify it?

Answer 12

so does the pi just get canceled out? where did that go...and yeah my college didnt do placemen tests so i needed calculus and they just gave it to me and now im beyond confused and switching my major next semester so i never have to do calc again

Answer 13

It'd be much easier for you to withdraw from this course:
V= (π/3 ) ( h/2 ) ²h
= (π/12) h³

Answer 14

i cant anymore that day passed...without anyone telling me about it..so i should take the derivative of that which meand h^3 would become 3h^2 and would (pi/12) be considered a number so it would just become 0?

Answer 15

V = (π/12) h³
->V' = (π/4) h² * h'
Now it's time to plug the numbers to find h'
( These types of problem is just touch base of calculus ! )

Answer 16

okay i understand im an idiot...thats why im changing my major and i dont know what to plug in where

Answer 17

sorry i just dont know what im supposed to even be finding with this equation im so losttt

Answer 18

v' = 50 ft³/min, h = 13 ft

Answer 19

so the answer is .377

Answer 20

Finally, h' = .38 ft/min

Answer 21

thanks a lot now i have at least one done