Question

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.

Answer 1

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:

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