Analysis and Approaches for IBDP Maths Ebook 1 | Page 145

Front Page
48
Paper 2 Section A – Percentage problems
12
Example
A balloon in the shape of a sphere is filled with gas until the radius is 10 cm.
(a)
Calculate the volume of the balloon.
The volume of the balloon is increased by 25%.
[2]
(b)
Calculate the radius of the balloon following this increase.
[4]
Solution
(a)
(b)
The volume
� 4 3
3 r
4 (10)
3
�
3 �
(A1) for substitution
� 4188.790205
3
� 4190 cm
A1 N2
4 3
V � � r
3
4188.790205 (1 25%)
4
3 3
r � 1250
(M1) for finding
r � 10.77217345
r � 10.8 cm
A1 N2
3
� � � (M2) for valid approach
3
r
[2]
[4]
Exercise 48
1. A plastic toy is in the shape of a sphere with radius 15 cm.
(a)
Calculate the total surface area of the plastic toy.
The plastic toy is enlarged such that its total surface area is increased by 30%.
[2]
(b)
Calculate the radius of the plastic toy following this increase.
[4]
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