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 183392 mℓ of water. The height of the water level in Container R is 1 cm higher than that in Container Q. Height of Container R is 68 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 R in litres?
2. What is the volume of water in the container now in litres?

(a)
²₃ of Container R = 183392 mℓ
¹₃ of Container R = 183392 ÷ 2 = 91696 mℓ
³₃ of Container R = 91696 x 3 = 275088 mℓ

1 ℓ = 1000 mℓ

Capacity of Container R = 275088 mℓ = 275.088 ℓ

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

Height of Container R not filled
= ¹₃ x 68 cm
= 22.666666666667 cm

Height of Container Q
= 68 - 22.666666666667 - 1
= 44.333333333333 cm

Volume of remaining water in Container Q
= 44.333333333333 x 44.333333333333 x 27
= 53066.999999999 cm³ 

Volume of remaining water in Container R
= 68 x 68 x 27
= 124848 cm³ 

Total volume of remaining water in the container
= 53066.999999999 + 124848
= 177915 cm³

1 ℓ = 1000 cm³
177915 cm³ = 177.915 ℓ

Answer(s): (a) 275.088 ℓ; (b) 177.915 ℓ