A 3D printer extrudes plastic filament at a constant rate of 8 millimeters per second. Wha… — SAT

A 3D printer extrudes plastic filament at a constant rate of $8$ millimeters per second. What is this rate, in meters per hour?

A
$0.48$
B
$2.88$
$28.8$ Answer
D
$28,800$

Answer

The rate is

28.8

meters per hour.

To convert the rate from millimeters per second to meters per hour, we apply the unit conversion factors. We convert millimeters to meters by dividing by

1000

, and convert seconds to hours by multiplying by

3600

. This gives:

8\text{ mm/s} \times \frac{1\text{ m}}{1000\text{ mm}} \times \frac{3600\text{ s}}{1\text{ hour}} = 8 \times 3.6 = 28.8\text{ meters per hour}

Step-by-Step Solution

Convert the length unit from millimeters to meters.

Since

1\text{ meter} = 1000\text{ millimeters}

, a rate of

8\text{ millimeters per second}

is equal to

\frac{8}{1000} = 0.008\text{ meters per second}

To convert from a smaller unit (millimeters) to a larger unit (meters), divide by the conversion factor of

1000

Convert the time unit from seconds to hours.

Since

1\text{ hour} = 3600\text{ seconds}

, a rate of

0.008\text{ meters per second}

is equal to

0.008 \times 3600 = 28.8\text{ meters per hour}

To find the distance printed in one hour, multiply the distance printed in one second by the number of seconds in one hour (

3600

Key Concept

Unit Conversions

Alternative Method

We can combine the conversion steps into a single conversion factor:

\frac{3600\text{ seconds/hour}}{1000\text{ millimeters/meter}} = 3.6\text{ (meters \cdot seconds) / (millimeters \cdot hour)}

. Multiplying the rate of

8\text{ mm/s}

3.6

gives the rate directly as

28.8\text{ m/h}

Estimated Time:1m 0s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

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