Question

Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 13 cm.
a. What is the volume of the cylinder? Explain your method for finding the volume.
b. What is the total volume of the three balls? Explain your method for finding the total volume.
c. What percent of the volume of the container is occupied by the three balls? Explain how you would find the percent.

Answer 1

If the diameter of one ball is 13 cm, to find the height of the cylinder, multiply it by 3

Answer 2

The diameter of the base of the cylinder will also be 13 cm

Answer 3

To find the total volume of the three balls, find teh volume for one, then multiply it by 3

Answer 4

the percent is volume of balls/volume of cylinder, convert decimal to percent

Answer 5

so a is 5176.6

Answer 6

yes, but I would leave it in pi form

Answer 7

so divide it by 3.14?

Answer 8

no, that wouldn't be accurate. It's 1647.75pi

Answer 9

and b is 1150.35?

Answer 10

1150.4*

Answer 11

yes, but again, leave in pi form, so 2197/6 pi

Answer 12

huh?

Answer 13

actually, no

Answer 14

You forgot to multiply by 3

Answer 15

1098.5 pi

Answer 16

thats just what google told me

Answer 17

Well, that's the volume of one sphere. you want the volume of alll three spheres

Answer 18

now what's c?

Answer 19

3295.5

Answer 20

=b?

Answer 21

no...i already gave b. it's 1098.5 pi

Answer 22

1098.5 pi/1647.75pi?

Answer 23

yes

Answer 24

the pis cancel out...you're left with 1098.5/1647.75 = ?

Answer 25

0.6666464376744751

Answer 26

0.7

Answer 27

I got .6666666666666666666 (basically 2/3)

Anyway, that's about 66.7%

Answer 28

vol of cyl = pi r^2 *6r = 6 pi r^3
vol of spheres = 3 * 4/3 pi r^3 = 4 pi r^3

ratio = exactly 2/3