The figure, not drawn to scale, is made of two connected cubical containers, N and P. Container N is sealed at the top and completely filled to the brim. Container P is ⁴₅ filled with 109868 mℓ of water. The height of the water level in Container P is 4 cm higher than that in Container N. Height of Container P is 65 cm. Water is then drained from the container and the height of the water level from the base falls to 29 cm.

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

(a)
⁴₅ of Container P = 109868 mℓ
¹₅ of Container P = 109868 ÷ 4 = 27467 mℓ
⁵₅ of Container P = 27467 x 5 = 137335 mℓ

1 ℓ = 1000 mℓ

Capacity of Container P = 137335 mℓ = 137.335 ℓ

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

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

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

Volume of remaining water in Container N
= 48 x 48 x 29
= 66816 cm³ 

Volume of remaining water in Container P
= 65 x 65 x 29
= 122525 cm³ 

Total volume of remaining water in the container
= 66816 + 122525
= 189341 cm³

1 ℓ = 1000 cm³
189341 cm³ = 189.341 ℓ

Answer(s): (a) 137.335 ℓ; (b) 189.341 ℓ