To determine the volume of the bookend, we need to compare the given options to see which one makes sense based on standard volume calculations. The volume of a rectangular prism can be computed using the formula:
[tex]\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \][/tex]
The given answer choices for the volume are:
A. [tex]\( 108 \)[/tex] cubic inches
B. [tex]\( 5\sqrt{3} + 9\sqrt{2} \)[/tex] cubic inches
C. [tex]\( 216 \)[/tex] cubic inches
D. [tex]\( 36\sqrt{12} \)[/tex] cubic inches
First, let's assess each of these options.
1. Option A: [tex]\( 108 \)[/tex] cubic inches
This is a straightforward numerical value.
2. Option B: [tex]\( 5\sqrt{3} + 9\sqrt{2} \)[/tex] cubic inches
We can evaluate this expression approximately:
[tex]\[
5\sqrt{3} \approx 5 \times 1.732 \approx 8.66
\][/tex]
[tex]\[
9\sqrt{2} \approx 9 \times 1.414 \approx 12.726
\][/tex]
[tex]\[
5\sqrt{3} + 9\sqrt{2} \approx 8.66 + 12.726 = 21.388
\][/tex]
3. Option C: [tex]\( 216 \)[/tex] cubic inches
This is another straightforward numerical value.
4. Option D: [tex]\( 36\sqrt{12} \)[/tex] cubic inches
We can evaluate this expression approximately:
[tex]\[
\sqrt{12} \approx \sqrt{4 \times 3} = 2\sqrt{3} \approx 2 \times 1.732 = 3.464
\][/tex]
[tex]\[
36\sqrt{12} \approx 36 \times 3.464 = 124.708
\][/tex]
Given these computations:
- Option A: [tex]\( 108 \)[/tex] cubic inches
- Option B: [tex]\( \approx 21.388 \)[/tex] cubic inches
- Option C: [tex]\( 216 \)[/tex] cubic inches
- Option D: [tex]\( \approx 124.708 \)[/tex] cubic inches
The correct option which seems appropriate and likely for the volume of a bookend among the given choices is:
A. 108 cubic inches
