Question 549543
[The value of is 3.142, correct to three decimal places.]
[The volume of a sphere is πr
3
.]
The diagrams show two ways of packaging 4 identical balls.
The radius of each ball is 3 cm.
Diagram I shows a closed rectangular box with a square base.
Each ball touches the top, the bottom and two sides of the box.
Each ball also touches two other balls.
Diagram II shows a closed cylinder.
The balls touch the ends and the side of the cylinder.
(a) (i) Write down the dimensions of the rectangular box. [1]
6 by 6 by 24 cm
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(ii) Calculate the total surface area of the outside of this box. [2]
There are 6 sides.  2 are 6 by 6, 4 are 6 by 24
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(b) Calculate the total surface area of the outside of the cylinder. [2]
{{{Lateral area = 2*pi*r*h}}} sq cm
{{{Ends = pi*r^2}}} sq cm
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(c) Calculate the total volume of the 4 balls. [2]
{{{Vol = 4*pi*r^3/3}}} for each ball.
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(d) Calculate, correct to three decimal places, the value of
volume of the cylinder
{{{Vol = pi*r^2*h}}}
––––––––––––––––––– . [2]
volume of the box
Vol = 6*6*24 cc
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(e) Hence state which of the two containers has more space not occupied by the balls. [1]
The one with the largest volume.