Final answer:
Compacting the snowball to 4/5 of its original diameter decreases its volume to (4/5)³ times the original volume while maintaining the same mass, resulting in an increased density of the snowball.
Step-by-step explanation:
When compacting the snowball so that its linear dimensions are 4/5 of the original, we have to consider the effects on both volume and density. The volume of a sphere is calculated by the formula V = (4/3)πr³, where r is the radius. Reducing the linear dimensions by 4/5 means that every linear measurement, including the radius, becomes 4/5 of its original size. rnew = (4/5) * roriginal.
Therefore, the new volume Vnew is:
Vnew = (4/3)πrnew³
= (4/3)π((4/5) * roriginal)³
= (4/3)π((4/5)³) * roriginal³
= ((4/5)³) * Voriginal
This means that the new volume is (4/5)³ times the original volume. Since density is the ratio of mass to the volume, if the mass 350 grams remains constant and the volume decreases, the density increases.
Analyzing how this affects the snowball, as the volume gets smaller, the snowball gets more packed and therefore, its density increases. This results in a denser snowball even though its mass has not changed.