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

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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) About Me  (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): sqrt%28r%5E2+%2B+h%5E2%29 = s
where
r = radius of base of the pile
h = the height
therefore
sqrt%28r%5E2+%2B+h%5E2%29 = 6
Square both sides, isolate r:
r%5E2+%2B+h%5E2+=+6%5E2
r%5E2+%2B+h%5E2+=+36
r%5E2+=+36+-+h%5E2
The volume of a cone:
V = 1%2F3pi%2Ar%5E2%2Ah
replace r^2 with (36-h^2)
V = 1%2F3pi%2A%2836-h%5E2%29%2Ah
Graph this equation, find the max vol
+graph%28+300%2C+200%2C+-4%2C+8%2C+-100%2C+150%2C+.333%2Api%2A%2836-x%5E2%29%2Ax%29+
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