SOLUTION: Decreasing cube. Each of the three dimensions of a cube with sides of length s centimeters is decreased by a whole number of centimeters. The new volume in cubic centimeters is giv

Question 169865: Decreasing cube. Each of the three dimensions of a cube with sides of length s centimeters is decreased by a whole number of centimeters. The new volume in cubic centimeters is given by V(s) = s^3 -13s^2 +54s - 72.
a) Find V(10).
b) If the new width is s - 6 centimeters, then what are the new length and height?
c) Find the volume when s = 10 by multiplying the length, width, and height.

Can someone please help me with this problem. Thank you
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Decreasing cube. Each of the three dimensions of a cube with sides of length s centimeters is decreased by a whole number of centimeters. The new volume in cubic centimeters is given by V(s) = s^3 -13s^2 +54s - 72.
a) Find V(10).
Sub 10 for s
V(10) = 10^3 - 13*10^2 + 54*10 - 72
V(10) = 1000 - 1300 + 540 - 72
V(10) = 1540 - 1372 = 168 cc
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b) If the new width is s - 6 centimeters, then what are the new length and height?
The product of L x H = (s^3 -13s^2 +54s - 72)/(s-6) = s^2 - 7s + 12
Since that's integers, that's (s-3)*(s-4). There's no way to know which is L and which is H.
c) Find the volume when s = 10 by multiplying the length, width, and height.
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?? Wasn't that part a? Maybe it means:
(10-6)*(10-3)*(10-4)
= 4*7*6
= 168 cc
Must be, it matches.

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