The diagram shows 3 tanks of different dimensions, each separated by a partition. Tank P, measuring 45 m by 34 m by 24 m, is filled with water to its brim. Tank N is an empty cuboidal container with a length of 28 m. Slider 1 is lifted to release ²₃ of the water from Tank P to Tank N, after which the partition is slid down to separate Tank P and Tank N. Next, Slider 2 is removed and some water from Tank N flows into Tank M such that the height of the water level of Tank N and Tank M is 6 m.

1. What is the length of Container M?
2. How many m³ of water are there in Container N?

(a)
Volume of water in the Tank P that flows into the Container N
= 45 x 34 x 24 x ²₃ 
= 24480 m³ 

Base area of Tank N and Tank M
= 24480 ÷ 6
= 4080 m² 

Length of Tank M and Tank N
= 4080 ÷ 34
= 120 m

Length of Tank M
= 120 - 28
= 92 m

(b)
Volume of water in Tank N
= 28 x 34 x 6
= 5712 m³ 

Answer(s): (a) 92 m; (b) 5712 m³