The figure, not drawn to scale, is made of two connected cubical tanks, X and Y. Tank X is sealed at the top and completely filled to the brim. Tank Y is ²₃ filled with 147376 mℓ of water. The height of the water level in Tank Y is 2 cm higher than that in Tank X. Height of Tank Y is 63 cm. Water is then drained from the container and the height of the water level from the base falls to 31 cm.

1. What is the capacity of Tank Y in litres?
2. What is the volume of water in the tank now in litres?

(a)
²₃ of Tank Y = 147376 mℓ
¹₃ of Tank Y = 147376 ÷ 2 = 73688 mℓ
³₃ of Tank Y = 73688 x 3 = 221064 mℓ

1 ℓ = 1000 mℓ

Capacity of Tank Y = 221064 mℓ = 221.064 ℓ

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

Height of Tank Y not filled
= ¹₃ x 63 cm
= 21 cm

Height of Tank X
= 63 - 21 - 2
= 40 cm

Volume of remaining water in Tank X
= 40 x 40 x 31
= 49600 cm³ 

Volume of remaining water in Tank Y
= 63 x 63 x 31
= 123039 cm³ 

Total volume of remaining water in the tank
= 49600 + 123039
= 172639 cm³

1 ℓ = 1000 cm³
172639 cm³ = 172.639 ℓ

Answer(s): (a) 221.064 ℓ; (b) 172.639 ℓ