The figure, not drawn to scale, is made of two connected cubical containers, L and M. Container L is sealed at the top and completely filled to the brim. Container M is ²₃ filled with 183394 mℓ of water. The height of the water level in Container M is 3 cm higher than that in Container L. Height of Container M is 66 cm. Water is then drained from the container and the height of the water level from the base falls to 20 cm.

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

(a)
²₃ of Container M = 183394 mℓ
¹₃ of Container M = 183394 ÷ 2 = 91697 mℓ
³₃ of Container M = 91697 x 3 = 275091 mℓ

1 ℓ = 1000 mℓ

Capacity of Container M = 275091 mℓ = 275.091 ℓ

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

Height of Container M not filled
= ¹₃ x 66 cm
= 22 cm

Height of Container L
= 66 - 22 - 3
= 41 cm

Volume of remaining water in Container L
= 41 x 41 x 20
= 33620 cm³ 

Volume of remaining water in Container M
= 66 x 66 x 20
= 87120 cm³ 

Total volume of remaining water in the container
= 33620 + 87120
= 120740 cm³

1 ℓ = 1000 cm³
120740 cm³ = 120.74 ℓ

Answer(s): (a) 275.091 ℓ; (b) 120.74 ℓ