Question

Problem #2


The shape is a Rectangular Prism.
the volume is 5cm
the height is 2cm
the width is 4cm



Find the TOTAL surface area of the shape.

Answer 1

To find the total surface area of a rectangular prism, you can use the formula:

\[
\text{Surface Area} = 2(lw + lh + wh)
\]

where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.

From the problem, we have:
- Volume = \( 5 \, \text{cm}^3 \)
- Height \( h = 2 \, \text{cm} \)
- Width \( w = 4 \, \text{cm} \)

First, we can find the length \( l \) using the volume formula for a rectangular prism:

\[
\text{Volume} = l \times w \times h
\]

Substituting our known values:

\[
5 = l \times 4 \times 2
\]

\[
5 = 8l
\]

Now, solving for \( l \):

\[
l = \frac{5}{8} \, \text{cm}
\]

Now we can substitute \( l \), \( w \), and \( h \) back into the surface area formula:

- \( l = \frac{5}{8} \, \text{cm} \)
- \( w = 4 \, \text{cm} \)
- \( h = 2 \, \text{cm} \)

Calculating \( lw \), \( lh \), and \( wh \):

- \( lw = \frac{5}{8} \times 4 = \frac{20}{8} = 2.5 \, \text{cm}^2 \)
- \( lh = \frac{5}{8} \times 2 = \frac{10}{8} = 1.25 \, \text{cm}^2 \)
- \( wh = 4 \times 2 = 8 \, \text{cm}^2 \)

Putting it all into the surface area formula:

\[
\text{Surface Area} = 2(2.5 + 1.25 + 8)
\]

Calculating the sum:

\[
2.5 + 1.25 + 8 = 11.75 \, \text{cm}^2
\]

Then calculate the total surface area:

\[
\text{Surface Area} = 2 \times 11.75 = 23.5 \, \text{cm}^2
\]

Thus, the total surface area of the rectangular prism is:

\[
\boxed{23.5 \, \text{cm}^2}
\]