A crate in the shape of a right rectangular prism can hold 8 feet by 4 feet by 3 feet worth of material. At a particular hardware store, the price of brick is $1.20 per cubic foot. How much would it cost to completely fill the crate with bricks, such that there is no space remaining in the crate?

Options

A. 38.4
B. 115.2
C. 384
D. 1152

Answer

To find the total cost to fill the crate with bricks, we will follow these steps:

### Step 1: Calculate the Volume of the Crate
The volume \( V \) of a right rectangular prism (or cuboid) is calculated using the formula:

\[ V = \text{Length} \times \text{Breadth} \times \text{Height} \]

Given the dimensions of the crate:
- Length \( L = 8 \) feet
- Breadth \( B = 4 \) feet
- Height \( H = 3 \) feet

Substituting the values into the formula:

\[ V = 8 \, \text{ft} \times 4 \, \text{ft} \times 3 \, \text{ft} \]

Calculating this gives:

\[ V = 8 \times 4 = 32 \, \text{ft}^2 \]
\[ V = 32 \times 3 = 96 \, \text{ft}^3 \]

### Step 2: Determine the Cost of Filling the Crate
The cost of bricks is given as $1.20 per cubic foot. To find the total cost \( C \) to fill the crate, we multiply the volume by the cost per cubic foot:

\[ C = V \times \text{Cost per cubic foot} \]

Substituting the known values:

\[ C = 96 \, \text{ft}^3 \times 1.20 \, \text{dollars/ft}^3 \]

Calculating this gives:

\[ C = 96 \times 1.20 = 115.20 \, \text{dollars} \]

### Final Answer
The total cost to completely fill the crate with bricks is **$115.20**.

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