a preschool is shopping for sand for its sandbox. Box A is 8 inches wide by 15 inches long by 11 inches high. Box B is 7 inches wide by 13 inches long by 18 inches high. Which box has more sand? Apply the formula V=Bh to solve. Show your work.

1 answer

To determine which box has more sand, we will calculate the volume of each box using the formula for volume \( V = Bh \), where \( B \) is the area of the base and \( h \) is the height of the box.

Step 1: Calculate the volume of Box A

Box A dimensions:

  • Width = 8 inches
  • Length = 15 inches
  • Height = 11 inches

First, calculate the area of the base \( B_A \): \[ B_A = \text{Width} \times \text{Length} = 8 , \text{inches} \times 15 , \text{inches} = 120 , \text{square inches} \]

Now, use the height to find the volume: \[ V_A = B_A \times h = 120 , \text{square inches} \times 11 , \text{inches} = 1320 , \text{cubic inches} \]

Step 2: Calculate the volume of Box B

Box B dimensions:

  • Width = 7 inches
  • Length = 13 inches
  • Height = 18 inches

First, calculate the area of the base \( B_B \): \[ B_B = \text{Width} \times \text{Length} = 7 , \text{inches} \times 13 , \text{inches} = 91 , \text{square inches} \]

Now, use the height to find the volume: \[ V_B = B_B \times h = 91 , \text{square inches} \times 18 , \text{inches} = 1638 , \text{cubic inches} \]

Step 3: Compare the volumes of Box A and Box B

  • Volume of Box A: \( 1320 , \text{cubic inches} \)
  • Volume of Box B: \( 1638 , \text{cubic inches} \)

Conclusion: Box B has more sand, with a volume of 1638 cubic inches compared to Box A’s 1320 cubic inches.