Question

Given that the surface area of a rectangular prism is given by the formula SA = 2lw + 2lh + 2wh, what is the value of SA if h =

cm, l = 8 cm, and w = 6 cm?
Responses

A 55 cm^2

B 96 cm^2

C 110 cm^2

D 152 cm^2

Answer 1

To calculate the surface area (SA) of the rectangular prism using the formula:

\[
SA = 2lw + 2lh + 2wh
\]

Given:
- \( l = 8 \) cm
- \( w = 6 \) cm
- \( h \) is not specified with a numeric value.

If we assume \( h \) to represent a particular height, which should be provided to complete the calculation. Since it is not given in your question, I’ll proceed with a symbolic approach.

For now, substituting the given values into the formula without a numeric height \( h \):

1. Calculate \( 2lw \):

\[
2lw = 2 \times 8 \times 6 = 96 \text{ cm}^2
\]

2. Calculate \( 2lh \):

\[
2lh = 2 \times 8 \times h = 16h \text{ cm}^2
\]

3. Calculate \( 2wh \):

\[
2wh = 2 \times 6 \times h = 12h \text{ cm}^2
\]

Now, combine the terms:

\[
SA = 96 + 16h + 12h
\]

\[
SA = 96 + 28h
\]

Without the specific value for \( h \), we cannot provide an exact numeric answer. In a typical scenario, if \( h \) were to hold a value, you could directly substitute it into \( SA = 96 + 28h \) to find the surface area.

For example, if \( h = 2 \) cm:

\[
SA = 96 + 28 \times 2 = 96 + 56 = 152 \text{ cm}^2
\]

Thus based on responses provided, if \( h \) were to equal 2 cm, the answer would be:

**D. 152 cm²**

Please provide the value of \( h \) if there is a specific height to use.