SOLUTION: A solid block of yellow cedar used for carving is in the shape of a rectangular prism. It has dimensions of 20 cm long, 12 cm wide, and 10 cm in height. The carver wants to reduce

Question 759888: A solid block of yellow cedar used for carving is in the shape of a rectangular prism. It has dimensions of 20 cm long, 12 cm wide, and 10 cm in height. The carver wants to reduce the volume to 768 cm^3 by removing the same amount off all three dimensions. Write a polynomial function to represent this situation. Calculate how much he should remove from each dimension algebraically.
The answer is 4 cm is to be removed, I need to see the steps! ANY HELP APPRECIATED THANKS!
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Volume = length * width * height = 20*12*10 = 2400 cm^3
now we want the following
(20-x)*(12-x)*(10-x) = 768
multiplying and combining like terms we have
-x^3 +42x^2 -560x +1632 = 0
then take the first derivative f'
f' = -3x^2 +84x -560
and x = (-b +or- sqrt(b^2 -3ac)) / 3a note if b^2-3ac > 0 the cubic has a min and max
this is the case for this problem and 4 is the min

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