To determine which box has a greater volume, we need to first calculate the volume of each box using their respective dimensions.
1. Volume of Box X:
Box X has the following dimensions:
- Length: 6 centimeters
- Width: 5 centimeters
- Height: 9 centimeters
To find the volume of Box X, we use the formula for the volume of a rectangular prism:
[tex]\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\][/tex]
Substituting in the dimensions of Box X:
[tex]\[
\text{Volume of Box X} = 6 \, \text{cm} \times 5 \, \text{cm} \times 9 \, \text{cm} = 270 \, \text{cubic centimeters}
\][/tex]
2. Volume of Box Y:
Box Y has the following dimensions:
- Length: 4 centimeters
- Width: 10 centimeters
- Height: 7 centimeters
Using the same volume formula for a rectangular prism:
[tex]\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\][/tex]
Substituting in the dimensions of Box Y:
[tex]\[
\text{Volume of Box Y} = 4 \, \text{cm} \times 10 \, \text{cm} \times 7 \, \text{cm} = 280 \, \text{cubic centimeters}
\][/tex]
3. Comparing the Volumes:
- Volume of Box X: 270 cubic centimeters
- Volume of Box Y: 280 cubic centimeters
Between the two, the volume of Box Y (280 cubic centimeters) is greater than the volume of Box X (270 cubic centimeters).
Therefore, Box Y has a greater volume.
