To determine which box has more sand, we'll calculate the volume of both Box A and Box B using the formula for the volume of a rectangular prism, \( V = B \cdot h \), where \( B \) is the area of the base (length x width) and \( h \) is the height.
Step 1: Calculate the volume of Box A.
- Dimensions of Box A:
- Width = 9 inches
- Length = 13 inches
- Height = 15 inches
Calculate the area of the base (B) of Box A: \[ B_A = \text{Length} \times \text{Width} = 13 , \text{inches} \times 9 , \text{inches} = 117 , \text{square inches} \]
Now calculate the volume (V_A): \[ V_A = B_A \times h = 117 , \text{square inches} \times 15 , \text{inches} = 1755 , \text{cubic inches} \]
Step 2: Calculate the volume of Box B.
- Dimensions of Box B:
- Width = 6 inches
- Length = 12 inches
- Height = 20 inches
Calculate the area of the base (B) of Box B: \[ B_B = \text{Length} \times \text{Width} = 12 , \text{inches} \times 6 , \text{inches} = 72 , \text{square inches} \]
Now calculate the volume (V_B): \[ V_B = B_B \times h = 72 , \text{square inches} \times 20 , \text{inches} = 1440 , \text{cubic inches} \]
Step 3: Compare the volumes of Box A and Box B.
- Volume of Box A = 1755 cubic inches
- Volume of Box B = 1440 cubic inches
Conclusion: Box A has a larger volume than Box B. Therefore, Box A has more sand.
Final Answer: Box A has more sand. Volume of Box A is 1755 cubic inches, while volume of Box B is 1440 cubic inches.