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 ⁴₅ filled with 113908 mℓ of water. The height of the water level in Container Z is 2 cm higher than that in Container Y. Height of Container Z is 67 cm. Water is then drained from the container and the height of the water level from the base falls to 25 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)
⁴₅ of Container Z = 113908 mℓ
¹₅ of Container Z = 113908 ÷ 4 = 28477 mℓ
⁵₅ of Container Z = 28477 x 5 = 142385 mℓ

1 ℓ = 1000 mℓ

Capacity of Container Z = 142385 mℓ = 142.385 ℓ

(b)
Fraction of Container Z not filled
= 1 - ⁴₅
= ¹₅

Height of Container Z not filled
= ¹₅ x 67 cm
= 13.4 cm

Height of Container Y
= 67 - 13.4 - 2
= 51.6 cm

Volume of remaining water in Container Y
= 51.6 x 51.6 x 25
= 66564 cm³ 

Volume of remaining water in Container Z
= 67 x 67 x 25
= 112225 cm³ 

Total volume of remaining water in the container
= 66564 + 112225
= 178789 cm³

1 ℓ = 1000 cm³
178789 cm³ = 178.789 ℓ

Answer(s): (a) 142.385 ℓ; (b) 178.789 ℓ