The machine extrudes a certain number of meters of rod per minute. How many minutes does it run, and what total length does that produce?

Once you know the radius (in meters) and the total length, treat the rod as a cylinder and use $V = \pi r^2 h$ to find its volume.

After finding the volume in cubic meters, multiply by the density (kilograms per cubic meter) to get the mass in kilograms, then round as directed.

In Desmos, enter the full expression for the mass in kilograms using meters for all lengths:

950 * pi * (0.0125)^2 * (1.2 * 3 * 60)

Here, 0.0125 is the radius in meters, and 1.2 * 3 * 60 is the total length in meters.

Look at the numerical value Desmos gives for this expression (it should be a bit over 100) and then round that value to the nearest whole number to match one of the answer choices.

The rate is in meters per minute and the density is in kilograms per cubic meter, so we should work entirely in meters and minutes.

• Time: $3$ hours $=3\times 60=180$ minutes.
• Diameter: $2.5$ centimeters $=2.5/100=0.025$ meters.
• Radius: $r=\dfrac{0.025}{2}=0.0125$ meters.

The machine extrudes $1.2$ meters of rod each minute for $180$ minutes.

So the cylinder (rod) has radius $0.0125$ m and height (length) $216$ m.

Use the cylinder volume formula $V = \pi r^2 h$.

First compute $r^2$:

Then multiply by the height:

So the volume is

which is approximately $0.106$ cubic meters (using $\pi \approx 3.14$).

Mass equals density times volume. The density is $950$ kilograms per cubic meter:

Rounding $100.7$ to the nearest kilogram gives $101$ kilograms, so the correct answer choice is C) 101.