The figure, not drawn to scale, is made of two connected cubical tanks, P and Q. Tank P is sealed at the top and completely filled to the brim. Tank Q is ²₃ filled with 107642 mℓ of water. The height of the water level in Tank Q is 5 cm higher than that in Tank P. Height of Tank Q is 66 cm. Water is then drained from the container and the height of the water level from the base falls to 30 cm.

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

(a)
²₃ of Tank Q = 107642 mℓ
¹₃ of Tank Q = 107642 ÷ 2 = 53821 mℓ
³₃ of Tank Q = 53821 x 3 = 161463 mℓ

1 ℓ = 1000 mℓ

Capacity of Tank Q = 161463 mℓ = 161.463 ℓ

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

Height of Tank Q not filled
= ¹₃ x 66 cm
= 22 cm

Height of Tank P
= 66 - 22 - 5
= 39 cm

Volume of remaining water in Tank P
= 39 x 39 x 30
= 45630 cm³ 

Volume of remaining water in Tank Q
= 66 x 66 x 30
= 130680 cm³ 

Total volume of remaining water in the tank
= 45630 + 130680
= 176310 cm³

1 ℓ = 1000 cm³
176310 cm³ = 176.31 ℓ

Answer(s): (a) 161.463 ℓ; (b) 176.31 ℓ