SPM Mathematics 2018, Paper 2 (Questions 3 & 4)


Question 3 (4 marks):
Diagram 3 shows a garden path with a rectangular shape. There are 8 similar circular stepping stone built in the path.


Given the area of the path is 32 m2, find the diameter, in m, of one piece of stepping stone.

Solution:
Given the area of the path=32 m2=320000 cm2x(x+4)=320000x2+4x320000=0a=1, b=4, c=320000x=b±b24ac2ax=4±424(1)(320000)2(1)x=4±12800162x=4+1131.382   or   41131.382x=563.69   or   567.69 (ignored)Diameter of one piece of steppingstone=x=563.69 cm=5.64 m




Question 4 (4 marks):
Diagram 4 shows a composite solid formed by joining a quarter cylinder and a cuboid which lies on the horizontal plane.


It is given that the height of the cuboid is 9 cm and the volume of the composite solid is 100267 cm3.  
Using π=227 , calculate the height, in cm, of the quarter cylinder.


Solution:
V cuboid+14(V cylinder)=100267(6×6×9)+14(227×122×t)=70207324+7927t=702077927t=47527t=6Height of the quarter cylinder=6 cm


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