word problem

Question

Three balls with a diameter of 6.00 cm are dropped into a long rectangular box with a square cross section. The balls stack up one on top of the other and they just touch the sides of the box. The box is the right height so that the edge of the top ball is even with the top of the box. What percent of the box’s volume is empty? If water is poured into the box around the balls, how many ounces to the nearest 0.1 oz will it take to fill the empty space?

Answer 1

The volume of each ball is V_ball =(4/3)*pi*radius³.  The volume of all 3 balls is:

 

     3*V_ball = 3*(4/3)*pi*radius³ = 4*pi*radius³ = 4*(3.14)*(3 cm)³ = 339.3 cm³

 

The volume of the box is V_box = length*width*height.  Since the balls just fit into the base, which is square, and touch the sides, the base is 6 cm by 6 cm.  The height is the height of 3 balls = 3*(6 cm) = 18 cm.  The volume of the box then is:

 

     V_box = 6*6*18 = 648 cm³

 

The empty space in the box is"

 

     Empty Volume = V_box - 3V_ball

 

The percentage if empty volume is:

 

     % = 100%*(Empty Volume)/(V_box)

 

Can you finish it from here?