The figure, not drawn to scale, is made of two connected cubical containers, P and Q. Container P is sealed at the top and completely filled to the brim. Container Q is ²₃ filled with 114992 mℓ of water. The height of the water level in Container Q is 1 cm higher than that in Container P. Height of Container Q 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 Q in litres?
2. What is the volume of water in the container now in litres?

(a)
²₃ of Container Q = 114992 mℓ
¹₃ of Container Q = 114992 ÷ 2 = 57496 mℓ
³₃ of Container Q = 57496 x 3 = 172488 mℓ

1 ℓ = 1000 mℓ

Capacity of Container Q = 172488 mℓ = 172.488 ℓ

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

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

Height of Container P
= 66 - 22 - 1
= 43 cm

Volume of remaining water in Container P
= 43 x 43 x 20
= 36980 cm³ 

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

Total volume of remaining water in the container
= 36980 + 87120
= 124100 cm³

1 ℓ = 1000 cm³
124100 cm³ = 124.1 ℓ

Answer(s): (a) 172.488 ℓ; (b) 124.1 ℓ