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

Answer 1

To find out how many times larger the surface area of prism B is compared to prism A, we first need to calculate the surface area of each prism using the formula for the surface area of a rectangular prism:

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

### Step 1: Calculate the surface area of prism A
For prism A with dimensions \( l = 2, w = 4, h = 6 \):

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

Calculating each term:
- \( lw = 2 \times 4 = 8 \)
- \( lh = 2 \times 6 = 12 \)
- \( wh = 4 \times 6 = 24 \)

Now, summing these values:

\[
lw + lh + wh = 8 + 12 + 24 = 44
\]

Calculating the total surface area:

\[
\text{Surface Area}_A = 2 \times 44 = 88
\]

### Step 2: Calculate the surface area of prism B
For prism B with dimensions \( l = 6, w = 12, h = 18 \):

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

Calculating each term:
- \( lw = 6 \times 12 = 72 \)
- \( lh = 6 \times 18 = 108 \)
- \( wh = 12 \times 18 = 216 \)

Now, summing these values:

\[
lw + lh + wh = 72 + 108 + 216 = 396
\]

Calculating the total surface area:

\[
\text{Surface Area}_B = 2 \times 396 = 792
\]

### Step 3: Find how many times larger the surface area of prism B is than prism A
Now we can compare the surface areas:

\[
\text{Times larger} = \frac{\text{Surface Area}_B}{\text{Surface Area}_A} = \frac{792}{88} = 9
\]

Therefore, the surface area of prism B is **9 times larger** than the surface area of prism A.