To find how many times larger the surface area of prism B is compared to prism A, we need to calculate the surface area of both prisms using the formula for the surface area of a rectangular prism:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
Surface Area of Prism A
Given dimensions for prism A:
- \( l = 2 \)
- \( w = 4 \)
- \( h = 6 \)
Calculating the surface area:
\[ \text{Surface Area of A} = 2(lw + lh + wh) = 2(2 \cdot 4 + 2 \cdot 6 + 4 \cdot 6) \]
Calculating each term:
- \( lw = 2 \cdot 4 = 8 \)
- \( lh = 2 \cdot 6 = 12 \)
- \( wh = 4 \cdot 6 = 24 \)
Now summing these:
\[ 8 + 12 + 24 = 44 \]
Thus, the surface area of prism A is:
\[ \text{Surface Area of A} = 2 \cdot 44 = 88 \]
Surface Area of Prism B
Given dimensions for prism B:
- \( l = 6 \)
- \( w = 12 \)
- \( h = 18 \)
Calculating the surface area:
\[ \text{Surface Area of B} = 2(lw + lh + wh) = 2(6 \cdot 12 + 6 \cdot 18 + 12 \cdot 18) \]
Calculating each term:
- \( lw = 6 \cdot 12 = 72 \)
- \( lh = 6 \cdot 18 = 108 \)
- \( wh = 12 \cdot 18 = 216 \)
Now summing these:
\[ 72 + 108 + 216 = 396 \]
Thus, the surface area of prism B is:
\[ \text{Surface Area of B} = 2 \cdot 396 = 792 \]
Finding the Ratio
Now, to find how many times larger the surface area of prism B is than that of prism A:
\[ \text{Ratio} = \frac{\text{Surface Area of B}}{\text{Surface Area of A}} = \frac{792}{88} = 9 \]
Thus, prism B's surface area is 9 times larger than the surface area of prism A.
So, the answer is:
Prism B’s surface area is 9 times larger than the surface area of prism A.