The figure, not drawn to scale, is made of two connected cubical tanks, W and X. Tank W is sealed at the top and completely filled to the brim. Tank X is ²₃ filled with 105466 mℓ of water. The height of the water level in Tank X is 2 cm higher than that in Tank W. Height of Tank X is 60 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 Tank X in litres?
2. What is the volume of water in the tank now in litres?

(a)
²₃ of Tank X = 105466 mℓ
¹₃ of Tank X = 105466 ÷ 2 = 52733 mℓ
³₃ of Tank X = 52733 x 3 = 158199 mℓ

1 ℓ = 1000 mℓ

Capacity of Tank X = 158199 mℓ = 158.199 ℓ

(b)
Fraction of Tank X not filled
= 1 - ²₃
= ¹₃

Height of Tank X not filled
= ¹₃ x 60 cm
= 20 cm

Height of Tank W
= 60 - 20 - 2
= 38 cm

Volume of remaining water in Tank W
= 38 x 38 x 27
= 38988 cm³ 

Volume of remaining water in Tank X
= 60 x 60 x 27
= 97200 cm³ 

Total volume of remaining water in the tank
= 38988 + 97200
= 136188 cm³

1 ℓ = 1000 cm³
136188 cm³ = 136.188 ℓ

Answer(s): (a) 158.199 ℓ; (b) 136.188 ℓ