A cylindrical dispenser of capacity 6.8 ℓ was filled with passion fruit juice to its brim. The passion fruit juice in the dispenser was then dispensed into a cubical container of sides 18 cm, through a tap flowing at a rate of 105 mℓ /min. After 10 min, the tap was turned off and the container was ²₃ full.

1. What percentage of the passion fruit juice in the cylindrical dispenser was left? Round off your answer to the nearest 2 decimal places.
2. How many litres of passion fruit juice were there in the container at first? (1 ℓ = 1000 cm³)

(a)
Volume of passion fruit juice that was dispensed
= 105 x 10
= 1050 mℓ

1 ℓ = 1000 mℓ
1.05 ℓ = 1050 mℓ

Volume of passion fruit juice Left in the dispenser
= 6.8 - 1.05
= 5.75 ℓ

Percentage of passion fruit juice Left in the dispenser
= 5.75 ÷ 6.8 x 100
= 84.558823529412%
≈ 84.56% (to 2 decimal places)

(b)
Amount of passion fruit juice in the container in the end
= ²₃ x 18 x 18 x 18
= 3888 cm³

Amount of passion fruit juice in the container at first
= 3888 - 1050
= 2838 cm³

1000 cm³ = 1  ℓ
2838 cm³ = 2.838 ℓ

Answer(s): (a) 84.56%; (b) 2.838 ℓ