To determine how many times larger the surface area of prism B is compared to prism A, we first need to calculate the surface area of both rectangular prisms 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:
- Length (\(l\)) = 2
- Width (\(w\)) = 4
- Height (\(h\)) = 6
Substituting the values into the formula:
\[ \text{Surface Area of A} = 2(2 \times 4 + 2 \times 6 + 4 \times 6) \] \[ = 2(8 + 12 + 24) \] \[ = 2(44) \] \[ = 88 \]
Step 2: Calculate the surface area of Prism B
For Prism B:
- Length (\(l\)) = 6
- Width (\(w\)) = 12
- Height (\(h\)) = 18
Substituting in the values:
\[ \text{Surface Area of B} = 2(6 \times 12 + 6 \times 18 + 12 \times 18) \] \[ = 2(72 + 108 + 216) \] \[ = 2(396) \] \[ = 792 \]
Step 3: Find how many times larger the surface area of B is compared to A
Now we can find the ratio of the surface areas:
\[ \text{Ratio} = \frac{\text{Surface Area of B}}{\text{Surface Area of A}} = \frac{792}{88} \]
Calculating the ratio:
\[ \frac{792}{88} = 9 \]
Conclusion
The surface area of prism B is 9 times larger than the surface area of prism A.
\[ \text{Prism B's surface area is } 9 \text{ times larger than the surface area of prism A.} \]