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.SIXTH GRADE WORK

1 answer

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.

  • The dimensions of Box A are:

    • Width = 9 inches
    • Length = 13 inches
    • Height = 15 inches
  • First, we calculate the area of the base: \[ B_A = \text{Width} \times \text{Length} = 9 , \text{inches} \times 13 , \text{inches} = 117 , \text{square inches} \]

  • 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.

  • The dimensions of Box B are:

    • Width = 6 inches
    • Length = 12 inches
    • Height = 20 inches
  • Calculate the area of the base: \[ B_B = \text{Width} \times \text{Length} = 6 , \text{inches} \times 12 , \text{inches} = 72 , \text{square inches} \]

  • 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.