Apps. and Interpretation for IBDP Maths Ebook 1 | Page 212

Your Practice Set – Applications and Interpretation for IBDP Mathematics
(c)
(d)
(e)
dV
0
dr � 2
30�r��r
� 0
(M1) for setting equation
By considering the graph of
y 30�r �r
2
� � ,
r � 0 (Rejected) or r � 30 . (M1) for valid approach
Thus, the required radius is 30 cm. A1 N3
The maximum volume
2 1 3
�15 �(30) � �(30)
(A1) for substitution
3
3
� A1 N2
4500�
cm
The total surface area
2 2 2
� �(30) ��(30)( 30 � 15 )
(M1)(A1) for correct approach
� 5988.600017
2
� 5990 cm
A1 N3
(f) V � 3000�
2 1 3
15� r � � r � 3000�
(M1) for setting equation
3
2 1 3
15� r � �r
�3000�
� 0
3
By considering the graph of
2 1 3
y �15� r � �r
� 3000�
, r � 18.391106 or
3
r � 39.118693 . (M1) for valid approach
Thus, the required radii are 18.4 cm and 39.1 cm. A1 N3
[3]
[2]
[3]
[3]
Exercise 59
1. A cylindrical blueberry can of height h and radius r , with an open end removed, is
produced such that the total outer surface area A is
the can.
(a) (i) Express h in terms of r .
2
27�
cm . Let V be the volume of
(ii)
27 1 3
Show that V � �r � �r
.
2 2
[4]
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