Each of the three dimensions of a cube with sides of lenth s centimeters is decreased by a whole numer of centimeters. The new volume is 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 volune when s=10 by multiplying the length, width, and height.

a) To find V(10), we need to substitute the value of s = 10 into the expression V(s)=s^3-13s^2+54s-72.

V(10) = (10)^3 - 13(10)^2 + 54(10) - 72
= 1000 - 13(100) + 540 - 72
= 1000 - 1300 + 540 - 72
= -1300 + 540 - 72 + 1000
= -832 + 1000
= 168

Therefore, V(10) is equal to 168 cubic centimeters.

b) If the new width is s-6 centimeters, then the new length and height can still be found using the original side length s.

Since the original dimensions of the cube are decreased by a whole number of centimeters, the new length will be (s - 6) centimeters, and the new height will also be (s - 6) centimeters. Therefore, the new length and height are (s - 6) centimeters.

c) To find the volume when s = 10, we need to multiply the length, width, and height.

Given that the new width is s - 6 and the new length and height are also s - 6, the volume can be found as follows:

Volume = (s - 6) * (s - 6) * (s - 6)

When s = 10:

Volume = (10 - 6) * (10 - 6) * (10 - 6)
= 4 * 4 * 4
= 64

Therefore, the volume when s = 10 is 64 cubic centimeters.