The figure, not drawn to scale, is made of two connected cubical tanks, L and M. Tank L is sealed at the top and completely filled to the brim. Tank M is ²₃ filled with 129600 mℓ of water. The height of the water level in Tank M is 4 cm higher than that in Tank L. Height of Tank M is 60 cm. Water is then drained from the container and the height of the water level from the base falls to 37 cm.

1. What is the capacity of Tank M in litres?
2. What is the volume of water in the tank now in litres?

(a)
²₃ of Tank M = 129600 mℓ
¹₃ of Tank M = 129600 ÷ 2 = 64800 mℓ
³₃ of Tank M = 64800 x 3 = 194400 mℓ

1 ℓ = 1000 mℓ

Capacity of Tank M = 194400 mℓ = 194.4 ℓ

(b)
Fraction of Tank M not filled
= 1 - ²₃
= ¹₃

Height of Tank M not filled
= ¹₃ x 60 cm
= 20 cm

Height of Tank L
= 60 - 20 - 4
= 36 cm

Volume of remaining water in Tank L
= 36 x 36 x 37
= 47952 cm³ 

Volume of remaining water in Tank M
= 60 x 60 x 37
= 133200 cm³ 

Total volume of remaining water in the tank
= 47952 + 133200
= 181152 cm³

1 ℓ = 1000 cm³
181152 cm³ = 181.152 ℓ

Answer(s): (a) 194.4 ℓ; (b) 181.152 ℓ