A typical 3-D printer creates object by laying down layers of ink one on top of another. The average thckness of layer depends on the caliber of the printer. For one particular 3-D printer, the average thickness of a layer is 102`mum` (micrometers). When creating a 1-inch cube, the printer takes 6 second to lay down each layer of ink. Approximately how long should it take this printer to create a 1-inch cube? (There are 1,000,000 micrometers in a meter, and 1 inch is approximately equal to 0.0254 meters.)

Options

A. 12 minutes
B. 25 minutes
C. 40 minutes
D. 1 hour, 6 minutes

Explanation

To solve the problem of how long it takes a 3-D printer to create a 1-inch cube, we will follow these steps:

### Step 1: Convert 1 inch to micrometers.
1 inch is approximately equal to 0.0254 meters. Since there are 1,000,000 micrometers in a meter, we can convert inches to micrometers as follows:

\[ 1 \text{ inch} = 0.0254 \text{ meters} \times 1,000,000 \text{ micrometers/meter} \]

Calculating this gives:

\[ 1 \text{ inch} = 0.0254 \times 10^6 \text{ micrometers} = 25400 \text{ micrometers} \]

### Step 2: Calculate the number of layers in the cube.
The thickness of each layer is given as 102 micrometers. To find the number of layers in the cube, we divide the total thickness (in micrometers) by the thickness of one layer:

\[ \text{Number of layers} = \frac{25400 \text{ micrometers}}{102 \text{ micrometers}} \]

Calculating this gives:

\[ \text{Number of layers} \approx 249 \text{ layers} \]

### Step 3: Calculate the total time taken to create the cube.
The printer takes 6 seconds to lay down each layer. Therefore, the total time taken to create all the layers is:

\[ \text{Total time (seconds)} = \text{Number of layers} \times \text{Time per layer} \]

Substituting the values we have:

\[ \text{Total time} = 249 \text{ layers} \times 6 \text{ seconds/layer} = 1494 \text{ seconds} \]

### Step 4: Convert seconds to minutes.
To convert the total time from seconds to minutes, we divide by 60:

\[ \text{Total time (minutes)} = \frac{1494 \text{ seconds}}{60} \]

Calculating this gives:

\[ \text{Total time (minutes)} \approx 24.9 \text{ minutes} \]

### Step 5: Round the time to the nearest whole number.
Rounding 24.9 minutes gives us approximately 25 minutes.

### Final Answer:
The printer will take approximately **25 minutes** to create a 1-inch cube.

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