To find the volume of the shoebox using the formula \( V = B \times h \), we first need to calculate the area of the base \( B \) and then multiply it by the height \( h \).
Step 1: Calculate the area of the base \( B \)
The base is a rectangle with the following dimensions:
- Length = \( 1 \frac{1}{2} \) ft = \( \frac{3}{2} \) ft
- Width = \( \frac{3}{4} \) ft
The area of the base \( B \) is calculated as follows:
\[ B = \text{Length} \times \text{Width} = \frac{3}{2} \times \frac{3}{4} \]
To multiply the fractions:
\[ B = \frac{3 \times 3}{2 \times 4} = \frac{9}{8} \quad \text{(square feet)} \]
Step 2: Height of the shoebox \( h \)
Height \( h = \frac{1}{2} \) ft.
Step 3: Calculate the volume \( V \)
Now use the formula for volume:
\[ V = B \times h = \frac{9}{8} \times \frac{1}{2} \]
To multiply the fractions:
\[ V = \frac{9 \times 1}{8 \times 2} = \frac{9}{16} \quad \text{(cubic feet)} \]
Thus, the volume of the shoebox is
\[ \frac{9}{16} \text{ ft}^3 \]
So the correct response is:
9/16 ftĀ³