Analysis and Approaches for IBDP Maths Ebook 2 | Page 153
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Paper 1 Section B – Problems Involving 3-D Objects
11
Example
The figure below shows a box of candies in the shape of pentagonal prism. This box is
closed with five square faces, and the top face and bottom face of the box are regular
pentagons. Each pentagonal face are formed by five congruent isosceles triangles of equal
sides x cm .
(a)
(b)
Show that the area of the top face is
Hence, find the total surface area
x , sin36 and cos36 .
5sin 72
2
2 2
x cm .
It is given that the painting cost $C of a box of candies is
C � Asec36 cosec36 �500x
� 2600 .
[1]
2
A cm of the box, giving the answer in terms of
[6]
(c)
(d)
Show that the painting cost of the box attains its minimum when
25
x � .
1 � 2 tan 36
Hence, find the exact minimum painting cost of the box.
[7]
[2]
www.seprodstore.com
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