Apps. and Interpretation for IBDP Maths Ebook 1 | Page 184

Your Practice Set – Applications and Interpretation for IBDP Mathematics
49
Paper 1 – Composite Objects
Example
A museum is built in the shape of a cylinder with a hemispherical roof on the top. The
height of the cylinder is 18 m and its radius is 24 m.
(a)
Calculate the volume of the museum.
The hemispherical roof and the outer cylindrical wall are to be painted.
[4]
(b)
Calculate the area to be painted.
[3]
Solution
(a)
(b)
The volume
2 3 2
�
3 �r
� �r
h
(M2) for valid approach
2 (24)
3 (24)
2
� (18)
3 � � �
(A1) for substitution
� 61524.95053
3
� 61500 m
A1 N4
The area
2
�2�r
� 2�rh
(M1) for valid approach
2
�2 �(24) � 2 �(24)(18)
(A1) for substitution
� 6333.45079
2
� 6330 m
A1 N3
[4]
[3]
174
SE Production Limited