Nan Hua Primary School 2006 PSLE Math Prelim Question

Eight identical 5-cm cubes are placed in an empty rectangular tank of length 75cm and width 40cm. The tank is then filled with water running from a tap at the rate of 9 litres per minute. It takes 11 min to fill up 2/3 of the tank.

a) How much more water is needed to fill up the tank to its brim? (Express your answer in litres)
b) Find the height of the tank.


Volume of 1 cube ----- 5cm x 5cm x 5cm = 125 cubic cm.
Volume of 8 cubes ----- 125 cubic cm x 8 = 1000 cubic cm.

In 1 minute ---- 9 litres is filled in the tank.
In 11 mins ----- 99 litres (99 000 cubic cm) will be filled.
By 11 mins, 2/3 of the tank is filled

Volume of 2/3 of tank
99 000 cubic cm (water) + 1000 cubic cm (8 cubes)
= 100 000 cubic cm or 100 litres

Q(a) How much more water is needed to fill up the tank to its brim? (Express your answer in litres)

At 2/3 height of tank ----- 100 litres
At 1/3 height of tank ----- 100 litres divided by 2 = 50 litres

Answer: 50 litres of water more was needed.


Q(b) Find the height of the tank.

Volume of whole tank
100 litres (2/3 volume) + 50 litres (1/3 volume) = 150 litres

Height of tank
Volume = length x width x height
150 litres (150 000 ml) = 75cm x 40cm x height
Height = 150 000ml divided by (75cm x 40cm)
Height = 50cm

Answer: The height of the tank is 50cm.