SOLUTION: Problem Volume. The length, width, and height of a box are x, 2x, and 3x - 5 inches, respectively. Write a polynomial V(x) that represents its volume. Find V(3). This is what I h

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Problem Volume. The length, width, and height of a box are x, 2x, and 3x - 5 inches, respectively. Write a polynomial V(x) that represents its volume. Find V(3). This is what I h      Log On


   



Question 81296: Problem
Volume. The length, width, and height of a box are x, 2x, and 3x - 5 inches, respectively. Write a polynomial V(x) that represents its volume. Find V(3).
This is what I have.
V(x) = x^2(x + 2)(3x - 5)
When you put V(3) into the equation the volume= 180
I would appreciate any help with this question. Thank you.

Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Volume. The length, width, and height of a box are x, 2x, and 3x - 5 inches, respectively. Write a polynomial V(x) that represents its volume. Find V(3).
This is what I have.
V(x) = x^2(2x)(3x - 5)
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Then V(3) = 3^2(2*3)(3*5-5) = 9*6*10 = 540 in^3
============
Cheers,
Stan H.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Remember that the volume of a rectangular prism (a box) is given by:
V+=+L%2AW%2Ah
In this case, you have:
L = x inches.
W = 2x inches.
h = (3x-5) inches.So the volume of the box in your problem can be expressed by the function:
V%28x%29+=+x%282x%29%283x-5%29 or
V%28x%29+=+6x%5E3-10x%5E2 so...
V%283%29+=+6%283%29%5E3-10%283%29%5E2
V%283%29+=+6%2827%29-10%289%29
V%283%29+=+162-90
V%283%29+=+72cubic inches.