Analysis and Approaches for IBDP Maths Ebook 1 | Seite 141

46
Paper 2 Section A – Composite objects
Front Page
12
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
h
(M2) for valid approach
2 (24)
3 (24)
2
� (18)
3 � � �
(A1) for substitution
� 61524.95053
3
� 61500 m
A1 N3
The area
2
�2�r
� 2�rh
(M2) for valid approach
2
�2 �(24) � 2 �(24)(18)
� 6333.45079
2
� 6330 m
A1 N2
[4]
[3]
Exercise 46
1. A church is built in the shape of a cylinder with a roof in the shape of a circular cone on
the top. The height of the cylinder is 5 m and its radius is 12 m. The height of the circular
cone is 16 m.
(a)
Calculate the volume of the church.
The roof on the top of the church is to be painted.
[4]
(b)
Calculate the area that is to be painted.
[3]
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