A rectangular container, 70 cm by 50 cm by 40 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 7 : 4. If ⁵₇ 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
= 70 x 50 x 7
= 24500 cm³ 

7 u = 24500 cm³ 
1 u = 24500 ÷ 7 = 3500 cm³ 
4 u = 4 x 3500 = 14000 cm³ 

Volume of water in ⁵₇ of the barrel = 14000 cm³ 

Volume of the barrel
= 14000 ÷ ⁵₇
= 14000 x ⁷₅ 
= 19600 cm³ 

(b)
Volume of the container
= 70 x 50 x 40
= 140000 cm³ 

Number of barrels to fill the container
= 140000 ÷ 19600
= 7 r 2800

Minimum number of barrels to fill the container
= 7 + 1
= 8

Answer(s): (a) 19600 cm³; (b) 8