A rectangular prism has the following dimensions:

l=5a, w=2a
, and h=(a^2-3a^2+a)
. Use the formula V=(l)(w)(h)
to find the volume of the rectangular prism.

1 answer

To find the volume \( V \) of the rectangular prism, we will use the formula:

\[ V = l \times w \times h \]

Given the dimensions of the rectangular prism:

  • Length \( l = 5a \)
  • Width \( w = 2a \)
  • Height \( h = (a^2 - 3a^2 + a) \)

We first simplify the expression for height \( h \):

\[ h = a^2 - 3a^2 + a = -2a^2 + a \]

Now we can substitute the values of \( l \), \( w \), and \( h \) into the volume formula:

\[ V = (5a) \times (2a) \times (-2a^2 + a) \]

First, calculate \( (5a) \times (2a) \):

\[ (5a) \times (2a) = 10a^2 \]

Now substitute this back into the volume expression:

\[ V = 10a^2 \times (-2a^2 + a) \]

Next, we expand this expression:

\[ V = 10a^2 \times (-2a^2) + 10a^2 \times a \]

Calculating each term gives:

\[ = -20a^4 + 10a^3 \]

Thus, the volume \( V \) of the rectangular prism is:

\[ \boxed{-20a^4 + 10a^3} \]