A 3D printer uses a plastic filament at a constant rate of 2.5\text{ grams} per minute of … — SAT

A 3D printer uses a plastic filament at a constant rate of $2.5\text{ grams}$ per minute of printing time. The filament has a density of $1.25\text{ grams per cubic centimeter}$ . If the printer runs continuously for $4\text{ hours}$ , what is the total volume, in cubic centimeters, of the filament used?

A
8
480Cevap
C
600
D
750

Cevap

480

The correct answer is 480. First, convert the printing time from hours to minutes: 4 hours multiplied by 60 minutes per hour equals 240 minutes. Next, calculate the total mass of the filament used by multiplying the printing time by the usage rate: 240 minutes multiplied by 2.5 grams per minute equals 600 grams. Finally, convert the mass to volume by dividing the mass by the density: 600 grams divided by 1.25 grams per cubic centimeter equals 480 cubic centimeters.

Adım Adım Çözüm

Convert the printing time from hours to minutes.

240\text{ minutes}

Since the filament consumption rate is given in grams per minute, the total time must be in minutes. Multiplying

4\text{ hours}

60\text{ minutes per hour}

yields

240\text{ minutes}

Calculate the total mass of the filament used.

600\text{ grams}

Multiplying the total printing time of

240\text{ minutes}

by the consumption rate of

2.5\text{ grams per minute}

gives a total mass of

600\text{ grams}

Calculate the total volume of the filament used.

480\text{ cubic centimeters}

Divide the total mass of

600\text{ grams}

by the density of

1.25\text{ grams per cubic centimeter}

to find the volume:

\frac{600}{1.25} = 480\text{ cubic centimeters}

Anahtar Kavram

Multi-unit dimensional analysis involving rates, time, and density.

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