Monday, October 25, 2010

MGS 2010 P6 Prelim P2 Q17:

A tank contains some water up to a height of 10 cm. When 4 identical marbles are put into the tank, the water level rises by 8 cm. One marble is then removed from the tank and a metal block is put into the tank. The water level increases to 22 cm.
(a) Find the ratio of the volume of 1 marble to the metal block. [2 marks]
(b) If the base area of the tank is 450 cm², how much more is the volume of the metal block than that of two marbles? [3 marks]
[Answer given: (a) 1 : 3   (b) 900 cm³]



4 marbles  -->  8 cm

1 marble  -->  1/4  x  8  =  2 cm

8  -  2  =  6  cm

Metal block  -->  22  -  10  -  6 =  6 cm

2 : 6 = 1 : 3      Since base area of tank is the same

a) The ratio of the volume of 1 marble to the metal block is 1 : 3.


6  -  2 x 2  =  2 cm

450  x  2  = 900 cm3

b) The volume of the metal block is  900 cm3  more than 2 marbles.

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