The figure, not drawn to scale, is made of two connected cubical tanks, E and F. Tank E is sealed at the top and completely filled to the brim. Tank F is ²₃ filled with 135714 mℓ of water. The height of the water level in Tank F is 3 cm higher than that in Tank E. Height of Tank F is 65 cm. Water is then drained from the container and the height of the water level from the base falls to 36 cm.

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

(a)
²₃ of Tank F = 135714 mℓ
¹₃ of Tank F = 135714 ÷ 2 = 67857 mℓ
³₃ of Tank F = 67857 x 3 = 203571 mℓ

1 ℓ = 1000 mℓ

Capacity of Tank F = 203571 mℓ = 203.571 ℓ

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

Height of Tank F not filled
= ¹₃ x 65 cm
= 21.666666666667 cm

Height of Tank E
= 65 - 21.666666666667 - 3
= 40.333333333333 cm

Volume of remaining water in Tank E
= 40.333333333333 x 40.333333333333 x 36
= 58563.999999999 cm³ 

Volume of remaining water in Tank F
= 65 x 65 x 36
= 152100 cm³ 

Total volume of remaining water in the tank
= 58563.999999999 + 152100
= 210664 cm³

1 ℓ = 1000 cm³
210664 cm³ = 210.664 ℓ

Answer(s): (a) 203.571 ℓ; (b) 210.664 ℓ