A preschool is shopping for sand for its sandbox. Box A is 9 inches wide by 13 inches long by 15 inches high. Box B is 6 inches wide by 12 inches long by 20 inches high. Which box has more sand? Apply the formula V = B · h to solve. Show your work.(2 points)

Answer 1

To determine which box has 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.

Box A:

• Dimensions: 9 inches (width) × 13 inches (length) × 15 inches (height)

1. Calculate the area of the base \( B \) of Box A: \[ B_A = \text{width} \times \text{length} = 9 , \text{inches} \times 13 , \text{inches} = 117 , \text{square inches} \]

2. Now calculate the volume \( V_A \): \[ V_A = B_A \cdot h = 117 , \text{square inches} \times 15 , \text{inches} = 1755 , \text{cubic inches} \]

Box B:

• Dimensions: 6 inches (width) × 12 inches (length) × 20 inches (height)

1. Calculate the area of the base \( B \) of Box B: \[ B_B = \text{width} \times \text{length} = 6 , \text{inches} \times 12 , \text{inches} = 72 , \text{square inches} \]

2. Now calculate the volume \( V_B \): \[ V_B = B_B \cdot h = 72 , \text{square inches} \times 20 , \text{inches} = 1440 , \text{cubic inches} \]

Comparison:

• Volume of Box A: \( 1755 , \text{cubic inches} \)
• Volume of Box B: \( 1440 , \text{cubic inches} \)

Conclusion:

Box A has more sand since \( 1755 , \text{cubic inches} > 1440 , \text{cubic inches} \).