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[answered] 1) Gravel is being dumped from a conveyor belt at a rate of


1) Gravel is being dumped from a conveyor belt at a rate of 40ft^3/min. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 12 ft high?

The height is increasing at______ ft/min.

2)?

An open box is to be made out of a 12-inch by 14-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume.

Dimensions of the bottom of the box: ?
Height of the box:?


Let v be the volume, r be the radius of the base and h be the height.

 

v r 2h

 

3 Since 2r h, plug r h

 

2 h3

 

12 h 2 h

 

v 4

 

Plug h 12, v 40

 

4v

 

h 2

 

h

 

4 40 10

 

h ft/min 144 9

 

v The height increases at a...

 


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