The figure, not drawn to scale, is made of two connected cubical containers, G and H. Container G is sealed at the top and completely filled to the brim. Container H is ²₃ filled with 107952 mℓ of water. The height of the water level in Container H is 2 cm higher than that in Container G. Height of Container H is 69 cm. Water is then drained from the container and the height of the water level from the base falls to 30 cm.

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

(a)
²₃ of Container H = 107952 mℓ
¹₃ of Container H = 107952 ÷ 2 = 53976 mℓ
³₃ of Container H = 53976 x 3 = 161928 mℓ

1 ℓ = 1000 mℓ

Capacity of Container H = 161928 mℓ = 161.928 ℓ

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

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

Height of Container G
= 69 - 23 - 2
= 44 cm

Volume of remaining water in Container G
= 44 x 44 x 30
= 58080 cm³ 

Volume of remaining water in Container H
= 69 x 69 x 30
= 142830 cm³ 

Total volume of remaining water in the container
= 58080 + 142830
= 200910 cm³

1 ℓ = 1000 cm³
200910 cm³ = 200.91 ℓ

Answer(s): (a) 161.928 ℓ; (b) 200.91 ℓ