A rectangular container, 70 cm by 45 cm by 45 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 7 : 2. If ⁵₇ 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
= 70 x 45 x 12
= 37800 cm³ 

7 u = 37800 cm³ 
1 u = 37800 ÷ 7 = 5400 cm³ 
2 u = 2 x 5400 = 10800 cm³ 

Volume of water in ⁵₇ of the bucket = 10800 cm³ 

Volume of the bucket
= 10800 ÷ ⁵₇
= 10800 x ⁷₅ 
= 15120 cm³ 

(b)
Volume of the container
= 70 x 45 x 45
= 141750 cm³ 

Number of buckets to fill the container
= 141750 ÷ 15120
= 9 r 5670

Minimum number of buckets to fill the container
= 9 + 1
= 10

Answer(s): (a) 15120 cm³; (b) 10