The Northampton Volunteer Association has built a rectangular sandbox for a local elementary school and is ready to fill it with sand. The sandbox is 60 inches wide, 72 inches long, and will be filled 18 inches deep. Under the assumption that 1 bag of sand can fill 3,600 cubic inches of the sandbox, what is the minimum number of bags of sand they will need in order to fill the sandbox ?

Options

A. 1
B. 7
C. 12
D. 22

Answer

To find the minimum number of bags of sand needed to fill the sandbox, we will follow these steps:

### Step 1: Calculate the Volume of the Sandbox
The volume \( V \) of a rectangular prism (sandbox) can be calculated using the formula:
\[ V = L \times W \times H \]
where:
- \( L \) = length of the sandbox = 72 inches
- \( W \) = width of the sandbox = 60 inches
- \( H \) = height (depth) of the sandbox = 18 inches

Substituting the values:
\[ V = 72 \times 60 \times 18 \]

### Step 2: Perform the Multiplication
Now, we will calculate the volume:
\[ V = 72 \times 60 = 4320 \]
\[ V = 4320 \times 18 = 77760 \text{ cubic inches} \]

### Step 3: Determine the Volume of Sand per Bag
According to the problem, one bag of sand can fill 3600 cubic inches.

### Step 4: Calculate the Number of Bags Needed
To find the number of bags required, we divide the total volume of the sandbox by the volume that one bag can fill:
\[ \text{Number of bags} = \frac{V}{\text{Volume per bag}} = \frac{77760}{3600} \]

### Step 5: Perform the Division
Now, we will perform the division:
\[ \text{Number of bags} = \frac{77760}{3600} = 21.6 \]

### Step 6: Round Up to the Nearest Whole Number
Since we cannot have a fraction of a bag, we round up to the nearest whole number:
\[ \text{Minimum number of bags} = 22 \]

### Final Answer
The minimum number of bags of sand needed to fill the sandbox is **22**.

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