A rectangular container, 80 cm by 50 cm by 45 cm, is filled with water to a height of 11 cm. The ratio of the volume of water in the container to that in a barrel is 5 : 2. If ²₅ 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 11
= 44000 cm³ 

5 u = 44000 cm³ 
1 u = 44000 ÷ 5 = 8800 cm³ 
2 u = 2 x 8800 = 17600 cm³ 

Volume of water in ²₅ of the barrel = 17600 cm³ 

Volume of the barrel
= 17600 ÷ ²₅
= 17600 x ⁵₂ 
= 44000 cm³ 

(b)
Volume of the container
= 80 x 50 x 45
= 180000 cm³ 

Number of barrels to fill the container
= 180000 ÷ 44000
= 4 r 4000

Minimum number of barrels to fill the container
= 4 + 1
= 5

Answer(s): (a) 44000 cm³; (b) 5