Analysis and Approaches for IBDP Maths Ebook 2 | Page 155

(d)
By the first derivative test,
M1A1
25
25
25
x 0 � x � x � x �
1 � 2 tan 36 1 � 2 tan 36 1 � 2 tan 36
dC
� 0 �
dx
Thus, the painting cost of the box attains its
25
minimum when x � . AG
1 � 2 tan 36
The exact minimum painting cost
� 25 �
�10 � � (1 �2 tan 36 )
�1�
2 tan 36 �
� 25 �
�500�
��2600
�1�
2 tan 36 �
2
� 625 � � 25 �
�10� � �500� � � 2600
�1�2tan36 � �1�2tan36
�
� 6250 12500
2600
1�2tan36 � 1�2tan36
�
� 6250 �
�$ �2600 � �
� 1 � 2 tan 36 �
(M1) for substitution
A1
[7]
[2]
11
Exercise 47
1. The figure below shows a prism of height h with the base in the shape of sector. The
sector has radius r , and the angle subtended by the arc is � radians.
Let V � 50 and A be the volume and the total surface area of the prism respectively.
(a)
100
Show that h � .
2
r �
(b) Hence, express A in terms of r and � .
[2]
[3]
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145