Analysis and Approaches for IBDP Maths Ebook 2 | Page 156

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Consider the case when the arc length of the sector is equal to its radius.
(c)
(d)
Show that A attains its minimum when
r � 3
150 .
Hence, find the value of k if the minimum value of A is
k 3
22500 .
(e) When A attains its minimum, h � br , b� . Find the value of b .
[7]
[3]
[3]
2. In the figure, the solid consists of a hemisphere of radius r cm joined to the bottom of a
right circular cylinder of height
h cm and base radius r cm.
Let V and
respectively.
2
A � 125 cm be the volume and the total surface area of the prism
(a)
Show that
125 3
h� � r.
2� r 2
(b) Find the value of r when h: r� 11:1.
(c) Express V in terms of r and � .
(d)
(e)
Show that V attains its maximum when
5
r � .
�
Hence, find the value of k if the maximum value of V is
[2]
[4]
[3]
[5]
25
k� . [4]
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