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  m 2 =320000  cm 2 x( x+4 )=320000 x 2 +4x320000=0 a=1, b=4, c=320000 x= b± b 2 4ac 2a x= 4± 4 2 4( 1 )( 320000 ) 2( 1 ) x= 4± 1280016 2 x= 4+1131.38 2    or    41131.38 2 x=563.69   or   567.69 ( ignored ) Diameter of one piece of stepping stone=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  1002 6 7  cm 3 .  
Using  π= 22 7 , calculate the height, in cm, of the quarter cylinder.


Solution:
V cuboid+ 1 4 ( V cylinder )=1002 6 7 ( 6×6×9 )+ 1 4 ( 22 7 × 12 2 ×t )= 7020 7 324+ 792 7 t= 7020 7 792 7 t= 4752 7 t=6 Height of the quarter cylinder=6 cm


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