The figure, not drawn to scale, is made of two connected cubical containers, Y and Z. Container Y is sealed at the top and completely filled to the brim. Container Z is ²₃ filled with 136738 mℓ of water. The height of the water level in Container Z is 4 cm higher than that in Container Y. Height of Container Z is 66 cm. Water is then drained from the container and the height of the water level from the base falls to 23 cm.

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

(a)
²₃ of Container Z = 136738 mℓ
¹₃ of Container Z = 136738 ÷ 2 = 68369 mℓ
³₃ of Container Z = 68369 x 3 = 205107 mℓ

1 ℓ = 1000 mℓ

Capacity of Container Z = 205107 mℓ = 205.107 ℓ

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

Height of Container Z not filled
= ¹₃ x 66 cm
= 22 cm

Height of Container Y
= 66 - 22 - 4
= 40 cm

Volume of remaining water in Container Y
= 40 x 40 x 23
= 36800 cm³ 

Volume of remaining water in Container Z
= 66 x 66 x 23
= 100188 cm³ 

Total volume of remaining water in the container
= 36800 + 100188
= 136988 cm³

1 ℓ = 1000 cm³
136988 cm³ = 136.988 ℓ

Answer(s): (a) 205.107 ℓ; (b) 136.988 ℓ