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

Question 202840: 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) s3 13s2 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.
Have tried the following: For A.) v(10)=10^3-13(10)^2+54(10)-72 For B. and C. I am completely lost at where to even begin.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Hi there,

Something must have not been copied correctly because there are a lot of box symbols all over the page. So I'm going to make a lot assumptions of what the problem really is.

a)

Start with the given function.

Plug in (ie replace each "s" with 10).

Cube to get .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

b)

Start with the volume equation.

Plug in the given expressions

Divide both sides by .

Factor the numerator

Cancel out the common terms.

Simplify

Rearrange the equation

Factor

So the new length and height are and

c)

I'll let you attempt this one on your own. Repost if you still need help.

Note: the answer is going to be the same as the answer in part a) (so you'll have something to check)

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