To find how many times larger the surface area of prism B is compared to prism A, we first calculate the surface areas of both prisms using the formula for the surface area \( S \) of a rectangular prism:
\[ S = 2(lw + lh + wh) \]
Calculating Surface Area of Prism A:
- Dimensions:
- Length \( l_A = 2 \)
- Width \( w_A = 4 \)
- Height \( h_A = 6 \)
\[ S_A = 2(l_A w_A + l_A h_A + w_A h_A) \] \[ = 2(2 \cdot 4 + 2 \cdot 6 + 4 \cdot 6) \] \[ = 2(8 + 12 + 24) \] \[ = 2(44) \] \[ = 88 \]
Calculating Surface Area of Prism B:
- Dimensions:
- Length \( l_B = 6 \)
- Width \( w_B = 12 \)
- Height \( h_B = 18 \)
\[ S_B = 2(l_B w_B + l_B h_B + w_B h_B) \] \[ = 2(6 \cdot 12 + 6 \cdot 18 + 12 \cdot 18) \] \[ = 2(72 + 108 + 216) \] \[ = 2(396) \] \[ = 792 \]
Finding how many times larger the surface area of prism B is than prism A:
\[ \text{Factor} = \frac{S_B}{S_A} = \frac{792}{88} = 9 \]
Thus, the surface area of prism B is 9 times larger than the surface area of prism A.
Final Answer: Prism B's surface area is 9 times larger than the surface area of Prism A.