The figure, not drawn to scale, is made of two connected cubical containers, M and N. Container M is sealed at the top and completely filled to the brim. Container N is ²₃ filled with 101172 mℓ of water. The height of the water level in Container N is 1 cm higher than that in Container M. Height of Container N is 60 cm. Water is then drained from the container and the height of the water level from the base falls to 34 cm.

1. What is the capacity of Container N in litres?
2. What is the volume of water in the container now in litres?

(a)
²₃ of Container N = 101172 mℓ
¹₃ of Container N = 101172 ÷ 2 = 50586 mℓ
³₃ of Container N = 50586 x 3 = 151758 mℓ

1 ℓ = 1000 mℓ

Capacity of Container N = 151758 mℓ = 151.758 ℓ

(b)
Fraction of Container N not filled
= 1 - ²₃
= ¹₃

Height of Container N not filled
= ¹₃ x 60 cm
= 20 cm

Height of Container M
= 60 - 20 - 1
= 39 cm

Volume of remaining water in Container M
= 39 x 39 x 34
= 51714 cm³ 

Volume of remaining water in Container N
= 60 x 60 x 34
= 122400 cm³ 

Total volume of remaining water in the container
= 51714 + 122400
= 174114 cm³

1 ℓ = 1000 cm³
174114 cm³ = 174.114 ℓ

Answer(s): (a) 151.758 ℓ; (b) 174.114 ℓ