Answer:
A. 706.5 in^3
B. 22 or 35 marbles (see below)
Step-by-step explanation:
Volume of a Cylinder = [tex]\pi * r^2 * h[/tex]
where [tex]r[/tex] is the radius of the cylinder
where [tex]h[/tex] is the height of the cylinder
We know from the problem statement that [tex]r[/tex] is 5 inches and [tex]h[/tex] is 9 inches. With all the variables, we just plug into the equation.
V = [tex]\pi * (5)^2 * 9 = 225 * 3.14 = 706.5[/tex] in^3
V = 706.5 in^3
Part B.
The answer to this problem depends on if you've heard of sphere packing or packing efficiency in class or not. Essentially, when you put marbles into a jar, you can still see empty spaces in the jar even though the jar can no longer fit anymore marbles. The amount of an object that can fit in a particular space is subject to something called packing efficiency.
Liquids have a packing efficiency of 100% because if we think about pouring water into a jar, the water will take up all available space. The packing efficiency of spheres is dependent on the arrangement of the spheres. According to Wikipedia, the average packing efficiency of irregular spheres (randomly adding marbles) cannot exceed 63.4%. If you're in a class, look in your textbook for this number.
First, we use packing efficiency to find the actual volume taken up by the marbles and assign to V1.
V1 = packing efficiency * total Volume (part 1) = 63.4% * 706.5 = 447.921 in^3
Next, we can divide by the volume of marbles.
# marbles = V1 / V of marble = 447.921 / 20 = 22.39605 marbles
# marbles = 22 marbles
(round down cause can't have 2/5 of a marble)
Now, if everything I said about packing efficiency is as alien as Katy Perry's ET song, then chances are you just want the simple solution.
The number of marbles is just the amount of marbles that can fit in the volume of jar.
# marbles = V1 (part 1) / V of marble = 706.5 / 20 = 35.325 marbles
# marbles = 35 marbles
