Question

Given a rectangular prism labeled A
with the dimensions l=2
, w=4
, and h=6
, and a second prism labeled B
with the dimensions l=6
, w=12
, and h=18
, how many times larger will the surface area of prism B
be than prism A
?(1 point)
Prism B
’s surface area is
times larger than the surface area of prism A
.

Answer 1

To determine how many times larger the surface area of prism B is compared to prism A, we first need to calculate the surface areas of both prisms.

The formula for the surface area (SA) of a rectangular prism is:

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

### For Prism A:
- Dimensions: \( l = 2 \), \( w = 4 \), \( h = 6 \)

Calculating the surface area of Prism A:

\[
SA_A = 2(lw + lh + wh) = 2(2 \times 4 + 2 \times 6 + 4 \times 6)
\]
\[
= 2(8 + 12 + 24) = 2(44) = 88
\]
So, the surface area of Prism A is \( 88 \) square units.

### For Prism B:
- Dimensions: \( l = 6 \), \( w = 12 \), \( h = 18 \)

Calculating the surface area of Prism B:

\[
SA_B = 2(lw + lh + wh) = 2(6 \times 12 + 6 \times 18 + 12 \times 18)
\]
\[
= 2(72 + 108 + 216) = 2(396) = 792
\]
So, the surface area of Prism B is \( 792 \) square units.

### Comparing the Surface Areas:
Now, we find out how many times larger the surface area of prism B is than prism A:

\[
\text{Factor} = \frac{SA_B}{SA_A} = \frac{792}{88} = 9
\]

Thus, Prism B’s surface area is **9 times larger** than the surface area of Prism A.