To determine how many cubic feet of sand Maya needs to fill her sandbox, we need to find the volume of the sandbox. The formula for the volume of a rectangular prism (or sandbox) is given by:
[tex]\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Depth} \][/tex]
Let's break down the dimensions given:
- Length: [tex]\( 4 \frac{1}{2} \)[/tex] feet
- Width: 3 feet
- Depth: [tex]\( \frac{1}{2} \)[/tex] foot
First, we convert the mixed number into an improper fraction or a decimal for easier calculation:
- Length: [tex]\( 4 \frac{1}{2} \)[/tex] feet can be written as [tex]\( 4 + \frac{1}{2} = 4.5 \)[/tex] feet
Now we have:
- Length = 4.5 feet
- Width = 3 feet
- Depth = 0.5 feet
We substitute these values into the volume formula:
[tex]\[ \text{Volume} = 4.5 \times 3 \times 0.5 \][/tex]
We then perform the multiplication step-by-step:
1. Multiply the length by the width:
[tex]\[ 4.5 \times 3 = 13.5 \][/tex]
2. Multiply the result by the depth:
[tex]\[ 13.5 \times 0.5 = 6.75 \][/tex]
Therefore, Maya needs 6.75 cubic feet of sand to fill the sandbox completely.
The correct answer from the given choices is [tex]\( 6 \frac{3}{4} \)[/tex] cubic feet, as it equals 6.75 in decimal form.
