A rectangular container, 80 cm by 50 cm by 35 cm, is filled with water to a height of 7 cm. The ratio of the volume of water in the container to that in a barrel is 5 : 2. If ²₃ of the barrel is filled with water, find

1. the volume of the barrel.
2. the minimum number of such barrels to fill the container.

(a)
Volume of water in the container
= 80 x 50 x 7
= 28000 cm³ 

5 u = 28000 cm³ 
1 u = 28000 ÷ 5 = 5600 cm³ 
2 u = 2 x 5600 = 11200 cm³ 

Volume of water in ²₃ of the barrel = 11200 cm³ 

Volume of the barrel
= 11200 ÷ ²₃
= 11200 x ³₂ 
= 16800 cm³ 

(b)
Volume of the container
= 80 x 50 x 35
= 140000 cm³ 

Number of barrels to fill the container
= 140000 ÷ 16800
= 8 r 5600

Minimum number of barrels to fill the container
= 8 + 1
= 9

Answer(s): (a) 16800 cm³; (b) 9