Analysis and Approaches for IBDP Maths Ebook 1 | Page 143

Front Page
47
Paper 2 Section A – Remoulding problems
12
Example
A metal sphere has a radius 8.8 cm.
(a) Find the volume of the sphere expressing your answer in the form a� 10 k ,
1�a
� 10 and k � .
[3]
The sphere is to be melted down and remoulded into the shape of a cone with a height of
17 cm.
(b)
Find the radius of the base of the cone.
[3]
Solution
(a)
(b)
The volume
4 3
�
3 r
(M1) for valid approach
� 4 (8.8)
3
3 �
� 2854.543238
(A1) for correct value
� 2850
3 3
�2.85� 10 cm
A1 N3
V
1
3
1 2
2854.543238 � (17)
3 (A1) for substitution
2
r � 160.3463529
r � 12.66279404
r � 12.7 cm
A1 N3
2
� � r h
(M1) for valid approach
[3]
[3]
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