The figure, not drawn to scale, is made of two connected cubical tanks, Y and Z. Tank Y is sealed at the top and completely filled to the brim. Tank Z is ³₄ filled with 172293 mℓ of water. The height of the water level in Tank Z is 4 cm higher than that in Tank Y. Height of Tank Z is 68 cm. Water is then drained from the container and the height of the water level from the base falls to 24 cm.

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

(a)
³₄ of Tank Z = 172293 mℓ
¹₄ of Tank Z = 172293 ÷ 3 = 57431 mℓ
⁴₄ of Tank Z = 57431 x 4 = 229724 mℓ

1 ℓ = 1000 mℓ

Capacity of Tank Z = 229724 mℓ = 229.724 ℓ

(b)
Fraction of Tank Z not filled
= 1 - ³₄
= ¹₄

Height of Tank Z not filled
= ¹₄ x 68 cm
= 17 cm

Height of Tank Y
= 68 - 17 - 4
= 47 cm

Volume of remaining water in Tank Y
= 47 x 47 x 24
= 53016 cm³ 

Volume of remaining water in Tank Z
= 68 x 68 x 24
= 110976 cm³ 

Total volume of remaining water in the tank
= 53016 + 110976
= 163992 cm³

1 ℓ = 1000 cm³
163992 cm³ = 163.992 ℓ

Answer(s): (a) 229.724 ℓ; (b) 163.992 ℓ