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 ³₄ filled with 116226 mℓ of water. The height of the water level in Container R is 2 cm higher than that in Container Q. Height of Container R is 64 cm. Water is then drained from the container and the height of the water level from the base falls to 40 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)
³₄ of Container R = 116226 mℓ
¹₄ of Container R = 116226 ÷ 3 = 38742 mℓ
⁴₄ of Container R = 38742 x 4 = 154968 mℓ

1 ℓ = 1000 mℓ

Capacity of Container R = 154968 mℓ = 154.968 ℓ

(b)
Fraction of Container R not filled
= 1 - ³₄
= ¹₄

Height of Container R not filled
= ¹₄ x 64 cm
= 16 cm

Height of Container Q
= 64 - 16 - 2
= 46 cm

Volume of remaining water in Container Q
= 46 x 46 x 40
= 84640 cm³ 

Volume of remaining water in Container R
= 64 x 64 x 40
= 163840 cm³ 

Total volume of remaining water in the container
= 84640 + 163840
= 248480 cm³

1 ℓ = 1000 cm³
248480 cm³ = 248.48 ℓ

Answer(s): (a) 154.968 ℓ; (b) 248.48 ℓ