SOLUTION: hello please help me ans these question it is a revision of mathematics i was doing and got stuck. i am having an exam to write tomorrow. [The value of is 3.142, correct to t

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Question 549543: hello please help me ans these question it is a revision of mathematics i was doing and got stuck. i am having an exam to write tomorrow.

[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]
(ii) Calculate the total surface area of the outside of this box. [2]
(b) Calculate the total surface area of the outside of the cylinder. [2]
(c) Calculate the total volume of the 4 balls. [2]
(d) Calculate, correct to three decimal places, the value of
volume of the cylinder
�� . [2]
volume of the box
(e) Hence state which of the two containers has more space not occupied by the balls. [1]
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
[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
-------------------------
(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
--------------------
(b) Calculate the total surface area of the outside of the cylinder. [2]
sq cm
sq cm
-------------------------------
(c) Calculate the total volume of the 4 balls. [2]
for each ball.
-----------------
(d) Calculate, correct to three decimal places, the value of
volume of the cylinder

�� . [2]
volume of the box
Vol = 6*6*24 cc
------------------
(e) Hence state which of the two containers has more space not occupied by the balls. [1]
The one with the largest volume.