A rectangular container, 80 cm by 55 cm by 35 cm, is filled with water to a height of 12 cm. The ratio of the volume of water in the container to that in a bucket is 11 : 4. If ³₅ of the bucket is filled with water, find

1. the volume of the bucket.
2. the minimum number of such buckets to fill the container.

(a)
Volume of water in the container
= 80 x 55 x 12
= 52800 cm³ 

11 u = 52800 cm³ 
1 u = 52800 ÷ 11 = 4800 cm³ 
4 u = 4 x 4800 = 19200 cm³ 

Volume of water in ³₅ of the bucket = 19200 cm³ 

Volume of the bucket
= 19200 ÷ ³₅
= 19200 x ⁵₃ 
= 32000 cm³ 

(b)
Volume of the container
= 80 x 55 x 35
= 154000 cm³ 

Number of buckets to fill the container
= 154000 ÷ 32000
= 4 r 26000

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

Answer(s): (a) 32000 cm³; (b) 5