Sam in packing toy blocks into a crate. If each block is a cube with a side of 6 inches, and the crate is 1 foot high, 2 feet long, and 2 feet wide, what many blocks can sam fit into the crate?

Options

A. `6`
B. `12`
C. `24`
D. `32`

Answer

To find out how many toy blocks Sam can fit into the crate, we will follow these steps:

### Step 1: Calculate the volume of one toy block.
The toy block is a cube with each side measuring 6 inches. The volume \( V \) of a cube is given by the formula:
\[ V = \text{side}^3 \]
Substituting the side length:
\[ V = 6^3 = 6 \times 6 \times 6 = 216 \text{ cubic inches} \]

### Step 2: Convert the dimensions of the crate from feet to inches.
The dimensions of the crate are given as:
- Height = 1 foot
- Length = 2 feet
- Width = 2 feet

Since 1 foot = 12 inches, we convert the dimensions:
- Height in inches = \( 1 \times 12 = 12 \) inches
- Length in inches = \( 2 \times 12 = 24 \) inches
- Width in inches = \( 2 \times 12 = 24 \) inches

### Step 3: Calculate the volume of the crate.
The volume \( V \) of the crate can be calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Substituting the dimensions:
\[ V = 24 \times 24 \times 12 \]

Calculating step-by-step:
1. \( 24 \times 24 = 576 \)
2. \( 576 \times 12 = 6912 \)

So, the volume of the crate is \( 6912 \text{ cubic inches} \).

### Step 4: Calculate the total number of blocks that can fit into the crate.
To find the total number of blocks, we divide the volume of the crate by the volume of one block:
\[ \text{Total number of blocks} = \frac{\text{Volume of crate}}{\text{Volume of one block}} \]
Substituting the volumes:
\[ \text{Total number of blocks} = \frac{6912}{216} \]

Calculating this:
1. \( 6912 \div 216 = 32 \)

Thus, Sam can fit a total of **32 blocks** into the crate.

### Final Answer:
Sam can fit **32 blocks** into the crate.

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