Question

Question
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)

Math Short Answer Rubric (2 points)
This table shows the criteria for awarding points and the corresponding point values.
Points Awarded Criteria
2
The answer is correct. The student made no errors while solving.

The answer shows that the student used problem-solving skills and reasoning.

All work is shown or explained.

1
The answer is partially correct. The student made errors while solving.

The answer shows little problem-solving skills or reasoning.

Some work is shown or explained.

0 The question is not answered.


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Answer 1

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.**