Analysis and Approaches for IBDP Maths Ebook 1 | Seite 147

Front Page
49
Paper 2 Section B – Angle between
lines and planes in a 3-D object
12
Example
A solid metal cylinder has a base radius of 30 cm and a height of 45 cm.
(a)
(b)
Find the volume of the cylinder.
Find the total surface area of the cylinder.
[3]
[3]
The cylinder was melted and recast into a solid circular cone, shown in the following
diagram. The base radius OA is 40 cm.
(c) Find the exact value of the height, OV , of the cone.
(d) Find the size of angle VAO .
(e) Find the total surface area of the cone.
[3]
[2]
[4]
Solution
(a)
The volume
2
� �r h
(M1) for valid approach
2
� � (30) (45)
(A1) for substitution
� 127234.5025
3
� 127000 cm
A1 N3
[3]
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139