A cylindrical dispenser of capacity 5.7 ℓ was filled with grapefruit juice to its brim. The grapefruit juice in the dispenser was then dispensed into a cubical container of sides 18 cm, through a tap flowing at a rate of 180 mℓ /min. After 11 min, the tap was turned off and the container was ²₃ full.

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

(a)
Volume of grapefruit juice that was dispensed
= 180 x 11
= 1980 mℓ

1 ℓ = 1000 mℓ
1.98 ℓ = 1980 mℓ

Volume of grapefruit juice Left in the dispenser
= 5.7 - 1.98
= 3.72 ℓ

Percentage of grapefruit juice Left in the dispenser
= 3.72 ÷ 5.7 x 100
= 65.263157894737%
≈ 65.26% (to 2 decimal places)

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

Amount of grapefruit juice in the container at first
= 3888 - 1980
= 1908 cm³

1000 cm³ = 1  ℓ
1908 cm³ = 1.908 ℓ

Answer(s): (a) 65.26%; (b) 1.908 ℓ