To determine which box holds more sand, we need to calculate the volume of each box using the formula \( V = B \cdot h \), where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height.
Step 1: Calculate the volume of Box A.
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The dimensions of Box A are:
- Width = 9 inches
- Length = 13 inches
- Height = 15 inches
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First, we calculate the area of the base: \[ B_A = \text{Width} \times \text{Length} = 9 , \text{inches} \times 13 , \text{inches} = 117 , \text{square inches} \]
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Now, we can find the volume of Box A: \[ V_A = B_A \cdot h = 117 , \text{square inches} \times 15 , \text{inches} = 1755 , \text{cubic inches} \]
Step 2: Calculate the volume of Box B.
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The dimensions of Box B are:
- Width = 6 inches
- Length = 12 inches
- Height = 20 inches
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Calculate the area of the base: \[ B_B = \text{Width} \times \text{Length} = 6 , \text{inches} \times 12 , \text{inches} = 72 , \text{square inches} \]
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Now, we can find the volume of Box B: \[ V_B = B_B \cdot h = 72 , \text{square inches} \times 20 , \text{inches} = 1440 , \text{cubic inches} \]
Step 3: Compare the volumes of Box A and Box B.
- Volume of Box A: \( 1755 , \text{cubic inches} \)
- Volume of Box B: \( 1440 , \text{cubic inches} \)
Conclusion: Since \( 1755 , \text{cubic inches} > 1440 , \text{cubic inches} \), Box A has more sand than Box B.