Find the volume of a rectangular prism if the length is 4x, the width is 5x, and the height is x2 + x + 2. Use the formula
V = l ⋅ w ⋅ h, where l is length, w is width, and h is height, to find the volume.

Question

Find the volume of a rectangular prism if the length is 4x, the width is 5x, and the height is x2 + x + 2. Use the formula 
V = l ⋅ w ⋅ h, where l is length, w is width, and h is height, to find the volume.

tennistar · Answer

Can someone walk me through how to solve this?

anonymous · Answer

hows it going?

tennistar · Answer

Pardon?

anonymous · Answer

i'm not pardon... e.e haha alright well i see you need some help, shall we get started?

tennistar · Answer

Yes, if you could.

anonymous · Answer

okay so our sides are 4x, 5x, and x^2+x+2, correct?

tennistar · Answer

Correct

anonymous · Answer

okay so do we need the value of x? or no?

tennistar · Answer

No, the value of V

tennistar · Answer

Volume

anonymous · Answer

no do we need a whole number? or an equation?

tennistar · Answer

I think its best I give the answer choices so:  
 20x3 + 20x2 + 40x
 20x4 + 20x3 + 40x2
 20x4 + x + 29
 20x4 + 9x3 + 18x2

tennistar · Answer

But please help me solve it, don't just give me an answer. I would like to understand how one reaches the answer.

anonymous · Answer

yes i know, i wouldnt do that, but i see that we need an equation :) thanks that explained alot

tennistar · Answer

If I were to input the numbers into the given equation, I get v = (4x) * (x^2 + x +2) * (5x). Is that correct?

anonymous · Answer

and yes that is correct

tennistar · Answer

Alright, now how do I proceed?

anonymous · Answer

okay so when we multiply variables we add the exponents and multiply the numbers.... like so:

2x*3x=6x^2

tennistar · Answer

So what would we get from this equation?

anonymous · Answer

so first we start with: 

4x*5x(x^2+x+2)

so we use PEMDAS

anonymous · Answer

so as you see there is nothing we can do in the parenthesis so we now distribute the 5x throughout the parenthesis, like so:

4x*5x(x^2+x+2)

4x* (5x*x^2)+(5x*x)+(5x*2)

anonymous · Answer

do you see, how that's done?

tennistar · Answer

Yes, I do. Multiply 5x by each part of the equation with the parenthesis to distribute

tennistar · Answer

within*

anonymous · Answer

oh sorry i messed up,,, it was:

 4x*5x(x^2+x+2)

20x^2(x^2+x+2)

now distribute.. sorry, that was my bad.

tennistar · Answer

Ah ok, I solved it. Should be 20x^4 + 20x^3 + 40x, yes?

anonymous · Answer

yes :) good job