The figure, not drawn to scale, is made of two connected cubical containers, K and L. Container K is sealed at the top and completely filled to the brim. Container L is ²₃ filled with 104094 mℓ of water. The height of the water level in Container L is 1 cm higher than that in Container K. Height of Container L is 65 cm. Water is then drained from the container and the height of the water level from the base falls to 27 cm.

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

(a)
²₃ of Container L = 104094 mℓ
¹₃ of Container L = 104094 ÷ 2 = 52047 mℓ
³₃ of Container L = 52047 x 3 = 156141 mℓ

1 ℓ = 1000 mℓ

Capacity of Container L = 156141 mℓ = 156.141 ℓ

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

Height of Container L not filled
= ¹₃ x 65 cm
= 21.666666666667 cm

Height of Container K
= 65 - 21.666666666667 - 1
= 42.333333333333 cm

Volume of remaining water in Container K
= 42.333333333333 x 42.333333333333 x 27
= 48386.999999999 cm³ 

Volume of remaining water in Container L
= 65 x 65 x 27
= 114075 cm³ 

Total volume of remaining water in the container
= 48386.999999999 + 114075
= 162462 cm³

1 ℓ = 1000 cm³
162462 cm³ = 162.462 ℓ

Answer(s): (a) 156.141 ℓ; (b) 162.462 ℓ