The figure, not drawn to scale, is made of two connected cubical containers, U and V. Container U is sealed at the top and completely filled to the brim. Container V is ²₃ filled with 112744 mℓ of water. The height of the water level in Container V is 1 cm higher than that in Container U. Height of Container V is 63 cm. Water is then drained from the container and the height of the water level from the base falls to 32 cm.

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

(a)
²₃ of Container V = 112744 mℓ
¹₃ of Container V = 112744 ÷ 2 = 56372 mℓ
³₃ of Container V = 56372 x 3 = 169116 mℓ

1 ℓ = 1000 mℓ

Capacity of Container V = 169116 mℓ = 169.116 ℓ

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

Height of Container V not filled
= ¹₃ x 63 cm
= 21 cm

Height of Container U
= 63 - 21 - 1
= 41 cm

Volume of remaining water in Container U
= 41 x 41 x 32
= 53792 cm³ 

Volume of remaining water in Container V
= 63 x 63 x 32
= 127008 cm³ 

Total volume of remaining water in the container
= 53792 + 127008
= 180800 cm³

1 ℓ = 1000 cm³
180800 cm³ = 180.8 ℓ

Answer(s): (a) 169.116 ℓ; (b) 180.8 ℓ