The diagram shows 3 tanks of different dimensions, each separated by a partition. Tank R, measuring 42 m by 32 m by 29 m, is filled with water to its brim. Tank Q is an empty cuboidal container with a length of 30 m. Slider 1 is lifted to release ¹₃ of the water from Tank R to Tank Q, after which the partition is slid down to separate Tank R and Tank Q. Next, Slider 2 is removed and some water from Tank Q flows into Tank P such that the height of the water level of Tank Q and Tank P is 7 m.

1. What is the length of Tank P?
2. How many m³ of water are there in Tank Q?

(a)
Volume of water in the Tank R that flows into the Tank Q
= 42 x 32 x 29 x ¹₃ 
= 12992 m³ 

Base area of Tank Q and Tank P
= 12992 ÷ 7
= 1856 m² 

Length of Tank P and Tank Q
= 1856 ÷ 32
= 58 m

Length of Tank P
= 58 - 30
= 28 m

(b)
Volume of water in Tank Q
= 30 x 32 x 7
= 6720 m³ 

Answer(s): (a) 28 m; (b) 6720 m³