Apps. and Interpretation for IBDP Maths Ebook 1 | Page 222

Your Practice Set – Applications and Interpretation for IBDP Mathematics
A square-based pyramid is formed with height 15 and the base area equals to the area of
R .
(b)
Find the exact volume of the pyramid.
[2]
2. Consider the graph of
f x
� � � , where f( x) � 0 for 0�x
� 6. Let R be the
2
( ) �(9 ( x 3) )
region enclosed by the graph of f and the x -axis.
(a) Find the area of R in terms of � .
A sphere is formed such that its total surface area equals to the area of R .
[2]
(b)
Find the radius of the sphere.
[2]
2
3. Consider the graph of f ( x) � ( x � 4) (8 � x)
, where f( x) � 0 for 4�x
� 8. Let R be the
region enclosed by the graph of f and the x -axis.
(a) (i) Write down the integral representing the area of R .
(ii) Hence, find the exact area of R .
[2]
A prism is formed with height h and the cross-sectional area equals to the area of R . The
volume of the prism is 320.
(b) Find the value of h .
[2]
4. Consider the graph of
f ( x) ( x 8) ( x 16)
2 2
� � � , where ( ) 0
the region enclosed by the graph of f and the x -axis.
f x � for 12 �x
� 16 . Let R be
(a) Find the exact area of R .
[2]
A pyramid is formed with height h and the base area equals to five times the area of R .
The volume of the pyramid is 1024.
(b) Find the exact value of h .
[2]
212
SE Production Limited