To find the volume of the box, we need to use the formula for the volume of a rectangular prism:
[tex]\[ V = l \cdot w \cdot h \][/tex]
where [tex]\( l \)[/tex] is the length, [tex]\( w \)[/tex] is the width, and [tex]\( h \)[/tex] is the height. Given the dimensions of the box:
- Length ([tex]\( l \)[/tex]) = 19 inches (already in inches)
- Width ([tex]\( w \)[/tex]) = 1.7 feet (need to convert to inches)
- Height ([tex]\( h \)[/tex]) = 6 inches (already in inches)
First, we need to convert the width from feet to inches. Since 1 foot is equal to 12 inches, we multiply the width by 12:
[tex]\[ w = 1.7 \text{ feet} \times 12 \text{ inches/foot} = 20.4 \text{ inches} \][/tex]
Now, all the dimensions are in inches:
- Length ([tex]\( l \)[/tex]) = 19 inches
- Width ([tex]\( w \)[/tex]) = 20.4 inches
- Height ([tex]\( h \)[/tex]) = 6 inches
Next, we plug these values into the volume formula:
[tex]\[ V = 19 \text{ inches} \times 20.4 \text{ inches} \times 6 \text{ inches} \][/tex]
When we multiply these values together, we get:
[tex]\[ V = 2325.6 \text{ cubic inches} \][/tex]
Therefore, the volume of the box is:
[tex]\[ 2325.6 \text{ cubic inches} \][/tex]
The correct option is:
[tex]\[ 2325.6 \text{ cubic inches} \left( \text{in}^3 \right) \][/tex]
