The figure, not drawn to scale, is made of two connected cubical containers, C and D. Container C is sealed at the top and completely filled to the brim. Container D is ²₃ filled with 127544 mℓ of water. The height of the water level in Container D is 4 cm higher than that in Container C. Height of Container D is 69 cm. Water is then drained from the container and the height of the water level from the base falls to 29 cm.

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

(a)
²₃ of Container D = 127544 mℓ
¹₃ of Container D = 127544 ÷ 2 = 63772 mℓ
³₃ of Container D = 63772 x 3 = 191316 mℓ

1 ℓ = 1000 mℓ

Capacity of Container D = 191316 mℓ = 191.316 ℓ

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

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

Height of Container C
= 69 - 23 - 4
= 42 cm

Volume of remaining water in Container C
= 42 x 42 x 29
= 51156 cm³ 

Volume of remaining water in Container D
= 69 x 69 x 29
= 138069 cm³ 

Total volume of remaining water in the container
= 51156 + 138069
= 189225 cm³

1 ℓ = 1000 cm³
189225 cm³ = 189.225 ℓ

Answer(s): (a) 191.316 ℓ; (b) 189.225 ℓ