SOLUTION: A pile of sand is in a roughly conical pile. The slant edge of the pile is 6.0 m. a). What is the height of the pile when the volume of sand in it is at a maximum? b). A truck op

Question 512201: A pile of sand is in a roughly conical pile. The slant edge of the pile is 6.0 m.
a). What is the height of the pile when the volume of sand in it is at a maximum?
b). A truck operator contracted to shift the sand wants to know how many cubic metres there are. What answer should he be given? Justify your answer with reference to the situation described?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A pile of sand is in a roughly conical pile. The slant edge of the pile is 6.0 m.
a). What is the height of the pile when the volume of sand in it is at a maximum?
:
the slant dimension (s): = s
where
r = radius of base of the pile
h = the height
therefore
= 6
Square both sides, isolate r:

The volume of a cone:
V =

replace r^2 with (36-h^2)
V =

Graph this equation, find the max vol

Max volume is 87 cu/m, occurs when height = 3.46 meters

b). A truck operator contracted to shift the sand wants to know how many cubic metres there are. What answer should he be given? Justify your answer with reference to the situation described?
:
See above, there are 87 cu/meters to move
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