Similar Figures and Surface Area Practice Complete this assessment to review what you’ve learned. It will not count toward your grade. 2 of 52 of 5 Items 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 Skip to navigation page 16 of 17 Formula keypad has been closed. Press Control + Backslash to open it again.

1 answer

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.

\[ \text{Prism B's surface area is } 9 \text{ times larger than the surface area of prism A.} \]