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 . Remaining Attempts : 3

Answer 1

To find 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.

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

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

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

Calculating the surface area:

\[
SA_A = 2(2 \cdot 4 + 2 \cdot 6 + 4 \cdot 6)
\]

Calculating each term:

\[
= 2(8 + 12 + 24) = 2(44) = 88
\]

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:

\[
SA_B = 2(6 \cdot 12 + 6 \cdot 18 + 12 \cdot 18)
\]

Calculating each term:

\[
= 2(72 + 108 + 216) = 2(396) = 792
\]

So, the surface area of prism B is \( 792 \) square units.

**Now, to find how many times larger the surface area of prism B is compared to prism A:**

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

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