Expert: Richard J. Raridon - 3/26/2009

Question
QUESTION: 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 + 54 - 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.



ANSWER: V(s) is not a cubic function, and you have 54-72?   Are you sure that's the right function?  
a) just put in s=10 and calculate V(10)
b) the width, length and height of a cube are identical
c) same as (a)

---------- FOLLOW-UP ----------

QUESTION: Richard,

Sorry, the 54s

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.  

Answer
Your problem states that the dimensions are decreased by a whole number of centimeters.  So the new volume ought to be (s-a)^3 where
a is an integer.  However, to get close to the equation for V(s) you can use (s-4.16)^3 which gives s^3 -12.48s^2 +51.92s -72.  So something is wrong with the problem.