Question 170010: Please Help. Thank You.
Increasing cube. Each of the three sides of a cube with
sides of x centimeters is increased by a whole number of
centimeters. The new volume in cubic centimeters is
given by
V(X)= x^3 + 10x^2 + 31x + 30.
a) Find V(3).
b) If the new height is x + 2 centimeters, then what are the
new length and width?
c) Find the volume when x =3 by multiplying the length,
width, and height.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Increasing cube. Each of the three sides of a cube with
sides of x centimeters is increased by a whole number of
centimeters. The new volume in cubic centimeters is
given by
V(X)= x^3 + 10x^2 + 31x + 30.
:
a) Find V(3).
:
V(3)= 3^3 + 10(3^2) + 31(3) + 30.
V(3) = 27 + 90 + 93 + 30
V(x) = 240 cu/cm
:
:
b) If the new height is x + 2 centimeters, then what are the
new length and width?
:
Divide x^3 + 10x^2 + 31x + 30 by (x+2); using synthetic division:
......________________
-2 | 1 + 10 + 31 + 30
:
you get: x^2 + 8x + 15 as length * width
Factor this to get the length and the width
(x + 5)(x + 3)
:
:
c) Find the volume when x = 3 by multiplying the length, width, and height
:
Just substitute 3 for x in (x+2), (x+5), (x+3)
:
Multiply these these values to find the volume
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