a gumball machine is in the shape of a sphere with a radius of 9 inches. a store manager wants to fill up the machine with gumballs, which have a radius of 3/4in. how many gumballs will fit in the machine?

547
1642
1728
5832

Let's use the formula for spheres:
V= 4/3 pi*r^3

First find the volume of the machine.
V=4/3 pi 9^3
= 4/3 pi 729

I'm going to guess you need pi in decimal form: 3.141592

V= 4/3 * 3.14 * 729
approximately equal to 3052.08

Then find the volume of each gumball using the same formula:
V= 4/3 pi (3/4)^3
= 4/3 * 3.14 * 27/64
approximately equal to 1.77

Now you have the volume for one gumball.

Divide the volume of the machine by the volume of one gumball:

3052.08 / 1.77 = 1724.34

Now, that would usually be the answer, but you can't have 0.34 of a gumball! So round down to the whole number (1724) and there's your answer!

Also, keep in mind this is just an estimate since we're using 3.14 as pi. If you have a calculator with pi, you can plug that in and get a more accurate answer. So out of the options, I would say 1728 is the answer.

Hope this helps!