Video Transcript
In an experiment, a measuring
cylinder is filled to 25 cubic centimeters with metal ball bearings and another is
filled to 25 cubic centimeters with sand. The sand is then added to the
measuring cylinder with the metal ball bearings. What is the total volume of the
mixture of sand and metal ball bearings? (A) Less than 50 cubic centimeters,
(B) exactly 50 cubic centimeters, (C) more than 50 cubic centimeters.
Each of the measuring cylinders is
filled with a solid: one contains sand and the other contains metal ball
bearings. We want to know what the total
volume will be when the sand is added to the measuring cylinder with the metal ball
bearings. Let’s consider each of these
solids.
If we look at sand under a
microscope, we can see that sand is made up of small, closely packed, individual
sand grains. The sand grains are not connected,
and there is space between them. But when we look at the sand in the
measuring cylinder with the naked eye, we can’t see any of these gaps. The ball bearings, on the other
hand, are large and do not closely pack together. We can clearly see gaps between the
metal ball bearings and the walls of the measuring cylinder. So, even though the ball bearings
were added to the measuring cylinder until they reached 25 cubic centimeters, the
actual volume of the ball bearings is much less than 25 cubic centimeters, because
there is lots of empty space between the ball bearings.
When the sand is added to the
measuring cylinder with the metal ball bearings, the sand grains are small enough to
fit in the spaces between the ball bearings. Because the sand occupies these
once empty spaces, the total volume of the mixture will be less than 50 cubic
centimeters. So, the total volume of the mixture
of sand and metal ball bearings will be less than 50 cubic centimeters, answer
choice (A).
