To find out how much bigger the larger box is compared to the smaller box, we need to calculate the volumes of both boxes.
First, let's find the volume of the larger box, which has dimensions 7 feet by 12 feet by 9 feet.
\[ \text{Volume of larger box} = \text{Length} \times \text{Width} \times \text{Height} = 7 , \text{ft} \times 12 , \text{ft} \times 9 , \text{ft} \]
Calculating that:
\[ 7 \times 12 = 84 \] \[ 84 \times 9 = 756 , \text{ft}^3 \]
Now let's calculate the volume of the smaller box, which has dimensions 5 feet by 7 feet by 6 feet.
\[ \text{Volume of smaller box} = \text{Length} \times \text{Width} \times \text{Height} = 5 , \text{ft} \times 7 , \text{ft} \times 6 , \text{ft} \]
Calculating that:
\[ 5 \times 7 = 35 \] \[ 35 \times 6 = 210 , \text{ft}^3 \]
Now, we have the volumes of both boxes:
- Volume of the larger box: \(756 , \text{ft}^3\)
- Volume of the smaller box: \(210 , \text{ft}^3\)
To find out how much bigger the larger box is than the smaller box, we subtract the volume of the smaller box from the volume of the larger box:
\[ \text{Difference in volume} = \text{Volume of larger box} - \text{Volume of smaller box} = 756 , \text{ft}^3 - 210 , \text{ft}^3 \] \[ = 546 , \text{ft}^3 \]
Therefore, the volume of the larger box is 546 ft³ more than the volume of the smaller box.