Apps. and Interpretation for IBDP Maths Ebook 1 | Page 214

Your Practice Set – Applications and Interpretation for IBDP Mathematics
(b)
25 3 1 3
(ii) Show that V � r � r .
3 8
[5]
Find d V
dr . [2]
(c) Find the value of r when the volume reaches its maximum.
[3]
(d) Find the maximum volume of the box.
[2]
The density of a three-dimensional solid is defined as the ratio of its mass to its volume.
It is given that the mass of the box when its volume reaches its maximum, is 9 kg.
(e) Find the density of this box, giving the answer in the form a� 10 k , where
1�a
� 10 and k � .
[2]
4. An acrylic block in the shape of prism with height h is produced such that the volume V
is
3
168 cm . The cross-sectional area of the block is a quarter circle with radius r . Let A
be the total surface area of the block.
(a) (i) Express h in terms of r .
(b)
1 2 �1344 �1
(ii) Hence, show that A� � r � � � 336�
.
2 � � �r
[5]
Find d A
dr , giving the answer in terms of � . [2]
(c) Find the value of r when the total surface area reaches its minimum.
[3]
(d) Find the minimum total surface area of the block.
[2]
For an acrylic block with the total surface area reaches its minimum, painting buckets are
used to make paint on the surface of the block. It is given that each bucket contains an
amount of paint which can cover
2
25 cm of the surface.
(e)
Find the minimum number of painting buckets required.
[2]
204
SE Production Limited