Find the volume of a rectangular prism if the length is 3x2, the width is 2x, and the height is x2 + 3x + 5. Use the formula V = l ⋅ w ⋅ h, where l is length, w is width, and h is height, to find the volume.
A. 5x5 + 18x^4 + 30x^3
B. 5x6 + 18x^4 + 30x^3
C. 6x5 + 18x^4 + 30x^3
D. 6x6 + 18x^4 + 30x^3

Question

Find the volume of a rectangular prism if the length is 3x2, the width is 2x, and the height is x2 + 3x + 5. Use the formula V = l ⋅ w ⋅ h, where l is length, w is width, and h is height, to find the volume. 
 A. 5x5 + 18x^4 + 30x^3  
B. 5x6 + 18x^4 + 30x^3  
C. 6x5 + 18x^4 + 30x^3  
D. 6x6 + 18x^4 + 30x^3

jadedry · Answer

You have to multiply these equations: $$(3x^2) * (2x) * (x^2 +3x+5)$$ to find the volume.


Do you know how to proceed?

mathstudent55 · Answer

V = 3x^2 * 2x * (x^2 + 3x + 5)

Multiply the first two factors together, then multiply by the trinomial.

anonymous · Answer

I don't know how to do that

anonymous · Answer

heyyy

jadedry · Answer

Okay, that's fine.

Just start with the first two values:

$$3x^2 * 2x$$

What does that equal?

shikamaru11 · Answer

To calculate the volume of rectangular prism or cuboid, count the number of small cubes in one layer. Next count how many cubes are there in the next layer and in the layer next. This gives the total Volume-rectangular prism.......

shikamaru11 · Answer

To calculate the volume of rectangular prism or cuboid, count the number of small cubes in one layer. Next count how many cubes are there in the next layer and in the layer next. This gives the total Volume-rectangular prism.......

shikamaru11 · Answer

heyy have you got the figure >>>>>>

anonymous · Answer

6x^2

jadedry · Answer

Close, but incorrect. 

$$3x^2 * 2x$$ = $$6x^3$$

Now you need to multiply:

$$6x^3 * (x^2 +3x + 5)$$

shikamaru11 · Answer

it's C ......... just simple algebric multiplication ma'm 
$$3x ^{2} * 2x = 6x ^{3}   and then   6x ^{3} * x ^{2}+3x+5= 6x ^{5}+18x ^{4}+30x ^{3}$$
and you should know how to multiplyy powers............. :\

mathstudent55 · Answer

Keep in mind that $x = x^1$, so 

$3x^x \times 2x =$

$= 3x^2 \times 2x^1$

$= 6 x^{2 + 1} $

$= 6x^3$

jadedry · Answer

@mathstudent55 

Well put, thanks for the elaboration. c:

shikamaru11 · Answer

yeah the powers are added while multiplying............. :) @mathstudent55 Sir nice one and thnx all for the participation :D @Jadedry @mariyakelly  :) stay happy guys

mathstudent55 · Answer

Now, just like you multiplied 3x^2 * 2x, do

6x^3 * (x^2 + 3x + 5)

using the distributive property.

That means:

$6x^3 \times (x^2 + 3x + 5)$

$= 6x^3 \times x^2 + 6x^3 \times 3x + 6x^2 \times 5$

Do each multiplication in the line above and separate them with + signs

mathstudent55 · Answer

@Jadedry Thanks!

mathstudent55 · Answer

@Shikamaru11 Thanks!

shikamaru11 · Answer

no prob. Sir @mathstudent55 :)

anonymous · Answer

I'm not ever using this in life? don't tell me what I should now how to do, I reached out for help for a reason. Don't be annoying, thankyou for your help goodbye