Question

What is the volume of a shoebox that is 1 1/2 ft. long, 3/4 ft. wide, and 1/2 ft. tall? Apply the V=B×h formula to solve.(1 point)

3/4ft^3
1 1/8ft^3
2 3/4ft^3
9/16ft^3

Answer 1

To find the volume of the shoebox, we can use the formula \(V = B \times h\), where \(B\) is the area of the base and \(h\) is the height.

1. **Calculate the area of the base \(B\)**:
\[
B = \text{length} \times \text{width} = \left(1 \frac{1}{2} \text{ ft}\right) \times \left(\frac{3}{4} \text{ ft}\right)
\]
First, convert \(1 \frac{1}{2}\) to an improper fraction:
\[
1 \frac{1}{2} = \frac{3}{2}
\]
Therefore:
\[
B = \frac{3}{2} \times \frac{3}{4}
\]
To multiply:
\[
B = \frac{3 \times 3}{2 \times 4} = \frac{9}{8} \text{ ft}^2
\]

2. **Calculate the height \(h\)**:
\[
h = \frac{1}{2} \text{ ft}
\]

3. **Calculate the volume \(V\)**:
\[
V = B \times h = \frac{9}{8} \text{ ft}^2 \times \frac{1}{2} \text{ ft}
\]
Multiply:
\[
V = \frac{9 \times 1}{8 \times 2} = \frac{9}{16} \text{ ft}^3
\]

The volume of the shoebox is \(\frac{9}{16} \text{ ft}^3\).

So the answer is:

\[
\boxed{\frac{9}{16} \text{ ft}^3}
\]