The figure, not drawn to scale, is made of two connected cubical containers, E and F. Container E is sealed at the top and completely filled to the brim. Container F is ²₃ filled with 152816 mℓ of water. The height of the water level in Container F is 1 cm higher than that in Container E. Height of Container F is 63 cm. Water is then drained from the container and the height of the water level from the base falls to 40 cm.

1. What is the capacity of Container F in litres?
2. What is the volume of water in the container now in litres?

(a)
²₃ of Container F = 152816 mℓ
¹₃ of Container F = 152816 ÷ 2 = 76408 mℓ
³₃ of Container F = 76408 x 3 = 229224 mℓ

1 ℓ = 1000 mℓ

Capacity of Container F = 229224 mℓ = 229.224 ℓ

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

Height of Container F not filled
= ¹₃ x 63 cm
= 21 cm

Height of Container E
= 63 - 21 - 1
= 41 cm

Volume of remaining water in Container E
= 41 x 41 x 40
= 67240 cm³ 

Volume of remaining water in Container F
= 63 x 63 x 40
= 158760 cm³ 

Total volume of remaining water in the container
= 67240 + 158760
= 226000 cm³

1 ℓ = 1000 cm³
226000 cm³ = 226 ℓ

Answer(s): (a) 229.224 ℓ; (b) 226 ℓ