12.Sand falls from a conveyor belt at a rate of 14 m2 /min onto the top of a conical pile. The height of the pile is alwayscm min when the height is 4 mThe height is changing at a rate of(Type an exact answer, using t as needed.)three-eighths of the base diameter. How fast are the height and the radius changing when the pile is 4 m high?cm/min when the height is 4 m.The radius is changing at a rate of(Type an exact answer, usingas needed.)

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Asked Oct 14, 2019
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12.
Sand falls from a conveyor belt at a rate of 14 m2 /min onto the top of a conical pile. The height of the pile is always
cm min when the height is 4 m
The height is changing at a rate of
(Type an exact answer, using t as needed.)
three-eighths of the base diameter. How fast are the height and the radius changing when the pile is 4 m high?
cm/min when the height is 4 m.
The radius is changing at a rate of
(Type an exact answer, using
as needed.)
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12. Sand falls from a conveyor belt at a rate of 14 m2 /min onto the top of a conical pile. The height of the pile is always cm min when the height is 4 m The height is changing at a rate of (Type an exact answer, using t as needed.) three-eighths of the base diameter. How fast are the height and the radius changing when the pile is 4 m high? cm/min when the height is 4 m. The radius is changing at a rate of (Type an exact answer, using as needed.)

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Expert Answer

Step 1

Volume of a conical pile having radius r and height h is given by:

1
V= πh
3
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1 V= πh 3

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Step 2

And it is given that height of pile is three-eighths of diameter that is,

3
(2r)
3
h -r
4
so,
3
V =-nr
3
1
4
1
V =
4
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3 (2r) 3 h -r 4 so, 3 V =-nr 3 1 4 1 V = 4

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Step 3

Now, since the sand is falling at a rate of 1...

dV
- = 14
dt
d1
= 14
dt4
dr
(3r2
- = 14
dt
dr
56
dt 37mr2
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dV - = 14 dt d1 = 14 dt4 dr (3r2 - = 14 dt dr 56 dt 37mr2

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Math

Calculus

Derivative