**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.**

## 1 comment:

Wah! So difficult!

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