Analysis and Approaches for IBDP Maths Ebook 1 | Page 148

Your Practice Set – Analysis and Approaches for IBDP Mathematics
(b)
(c)
(d)
(e)
The total surface area
2
�2�r
� 2�rh
(M1) for valid approach
2
�2 �(30) � 2 �(30)(45)
(A1) for substitution
� 14137.16694
2
� 14100 cm
A1 N3
1
V
3
1
�
3 �
(A1) for substitution
OV � 75.9375 cm
A1 N3
2
� � r h
(M1) for valid approach
2
127234.5025 (40) (OV)
ˆ OV
tan VAO � OA
(M1) for tangent ratio
ˆ 75.9375
tan VAO �
40
VAO ˆ � 62.22202722
VAO ˆ � 62.2
A1 N2
The slant height l
2 2
� � (M1) for finding slant height
75.9375 40
� 85.82833976
The total surface area
2
��r
� �rl
(M1) for valid approach
2
��(40) � �(40)(85.82833976)
(A1) for substitution
� 15812.05551
2
� 15800 cm
A1 N2
[3]
[3]
[2]
[4]
Exercise 49
1. A solid metal hemisphere has a base radius of 10 cm.
(a) Find the volume of the hemisphere.
[3]
(b) Find the total surface area of the hemisphere.
[3]
Four identical hemispheres were melted and recast into a solid circular cone, shown in the
following diagram. The base diameter AB is 38 cm.
140
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