Golf balls also come in packages of three, but they are usually packaged in a rectangular box with a square bottom. The radius of each ball is about 2.2cm.

Question

The radius of each ball is about 2.2cm. the length and width of the box's square base are twice the radius and the height is six times the radius.

A. would you guess that there would be more or less empty space by percentage than there is in a tennis ball can. why?

B. use your procedure from question 4 to find the percentage of the golf ball box that is filed round volumes to the nearest hundredth.

Answer 1

Rather than guessing, we are going to calculate the answer.

A ball with radius R (in this case R = 2.2 cm) has a volume of

V_ball = (4/3) π R³

Each box has 3 balls in it, so the volume taken by the balls is

3V_ball = 4 π R³

On other hand, each box has volume of

V_box = 2R x 2R x 6R = 24 R³

Now we can calculate the share of the volume taken by the balls

3V_ball / V_box = 4πR³ / 24R³ = π/6

Converting the result into percents

%balls = 100% x 3.1416 / 6 ≈ 52.36%

%empty space = 100% - %balls = 47.64%

Finally %balls > %empty space