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.
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