Question

sand is poured on a conical pile at a rate of 20 m^3/min. The height of the pile is always equal to the radius of the base of the pile. When the pile is 3m high, how fast is the height of the pile increasing?

Answer 1

dv/dt=20 m^3/minute
we r given that radius=height, so radius=3=heoght :)
Volume of cone=1/3(πr^2h)
now Volume=1/3π9h
dv/dt=1/3(9)dh/dt
dv/dt=3dh/dt
dv/dt=3dh/dt
we know that dv/dt=20
so 20=3dh/dt
dh/dt=20/3

Answer 2

how did you get the now volume?

Answer 3

oh it's radius sorry :))

Answer 4

*the

Answer 5

it is given in the question that height of pike is ALWAYS equal to radius of pile :)

Answer 6

*pile

Answer 7

why was the π gone in dv/dt=1/3(9)dh/dt? :)

Answer 8

@imqwerty

Answer 9

yea pi shuld also come sry

Answer 10

the answer should be 20/3π? :)

Answer 11

yea

Answer 12

oh it's not in the choices :(

Answer 13

what r the choices?

Answer 14

the choices are : 1.42, 0.71, 0.66 and 1.32

Answer 15

something went wrng jst a min

Answer 16

oh it's supposed to be 20/9π :)

Answer 17

dv/dt = 1/3πr^(3)

Answer 18

how?

Answer 19

dv/dt = πr^(2)dh/dt

Answer 20

:O okay :)

Answer 21

dv/dt = π(9) dh/dt then plug in 20 for dv/dt

Answer 22

thank you guys for helping me :)

Answer 23

no prblm :D