The figure, not drawn to scale, is made of two connected cubical containers, Q and R. Container Q is sealed at the top and completely filled to the brim. Container R is ²₃ filled with 161492 mℓ of water. The height of the water level in Container R is 4 cm higher than that in Container Q. Height of Container R is 63 cm. Water is then drained from the container and the height of the water level from the base falls to 34 cm.

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

(a)
²₃ of Container R = 161492 mℓ
¹₃ of Container R = 161492 ÷ 2 = 80746 mℓ
³₃ of Container R = 80746 x 3 = 242238 mℓ

1 ℓ = 1000 mℓ

Capacity of Container R = 242238 mℓ = 242.238 ℓ

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

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

Height of Container Q
= 63 - 21 - 4
= 38 cm

Volume of remaining water in Container Q
= 38 x 38 x 34
= 49096 cm³ 

Volume of remaining water in Container R
= 63 x 63 x 34
= 134946 cm³ 

Total volume of remaining water in the container
= 49096 + 134946
= 184042 cm³

1 ℓ = 1000 cm³
184042 cm³ = 184.042 ℓ

Answer(s): (a) 242.238 ℓ; (b) 184.042 ℓ