The figure, not drawn to scale, is made of two connected cubical containers, W and X. Container W is sealed at the top and completely filled to the brim. Container X is ⁴₅ filled with 170764 mℓ of water. The height of the water level in Container X is 5 cm higher than that in Container W. Height of Container X is 60 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 X in litres?
2. What is the volume of water in the container now in litres?

(a)
⁴₅ of Container X = 170764 mℓ
¹₅ of Container X = 170764 ÷ 4 = 42691 mℓ
⁵₅ of Container X = 42691 x 5 = 213455 mℓ

1 ℓ = 1000 mℓ

Capacity of Container X = 213455 mℓ = 213.455 ℓ

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

Height of Container X not filled
= ¹₅ x 60 cm
= 12 cm

Height of Container W
= 60 - 12 - 5
= 43 cm

Volume of remaining water in Container W
= 43 x 43 x 25
= 46225 cm³ 

Volume of remaining water in Container X
= 60 x 60 x 25
= 90000 cm³ 

Total volume of remaining water in the container
= 46225 + 90000
= 136225 cm³

1 ℓ = 1000 cm³
136225 cm³ = 136.225 ℓ

Answer(s): (a) 213.455 ℓ; (b) 136.225 ℓ