The figure, not drawn to scale, is made of two connected cubical containers, V and W. Container V is sealed at the top and completely filled to the brim. Container W is ²₃ filled with 142748 mℓ of water. The height of the water level in Container W is 1 cm higher than that in Container V. Height of Container W is 69 cm. Water is then drained from the container and the height of the water level from the base falls to 40 cm.

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

(a)
²₃ of Container W = 142748 mℓ
¹₃ of Container W = 142748 ÷ 2 = 71374 mℓ
³₃ of Container W = 71374 x 3 = 214122 mℓ

1 ℓ = 1000 mℓ

Capacity of Container W = 214122 mℓ = 214.122 ℓ

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

Height of Container W not filled
= ¹₃ x 69 cm
= 23 cm

Height of Container V
= 69 - 23 - 1
= 45 cm

Volume of remaining water in Container V
= 45 x 45 x 40
= 81000 cm³ 

Volume of remaining water in Container W
= 69 x 69 x 40
= 190440 cm³ 

Total volume of remaining water in the container
= 81000 + 190440
= 271440 cm³

1 ℓ = 1000 cm³
271440 cm³ = 271.44 ℓ

Answer(s): (a) 214.122 ℓ; (b) 271.44 ℓ