The figure, not drawn to scale, is made of two connected cubical containers, J and K. Container J is sealed at the top and completely filled to the brim. Container K is ⁴₅ filled with 150928 mℓ of water. The height of the water level in Container K is 4 cm higher than that in Container J. Height of Container K is 65 cm. Water is then drained from the container and the height of the water level from the base falls to 37 cm.

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

(a)
⁴₅ of Container K = 150928 mℓ
¹₅ of Container K = 150928 ÷ 4 = 37732 mℓ
⁵₅ of Container K = 37732 x 5 = 188660 mℓ

1 ℓ = 1000 mℓ

Capacity of Container K = 188660 mℓ = 188.66 ℓ

(b)
Fraction of Container K not filled
= 1 - ⁴₅
= ¹₅

Height of Container K not filled
= ¹₅ x 65 cm
= 13 cm

Height of Container J
= 65 - 13 - 4
= 48 cm

Volume of remaining water in Container J
= 48 x 48 x 37
= 85248 cm³ 

Volume of remaining water in Container K
= 65 x 65 x 37
= 156325 cm³ 

Total volume of remaining water in the container
= 85248 + 156325
= 241573 cm³

1 ℓ = 1000 cm³
241573 cm³ = 241.573 ℓ

Answer(s): (a) 188.66 ℓ; (b) 241.573 ℓ