A rectangular container 120 cm by 50 cm by 49 cm was 10% filled with water. A tap was turned on to fill it up with water at a rate of 9 ℓ/min. Every 30 seconds after the tap was turned on, an iron ball of volume 200 cm3 was added to the container. How many iron balls of the same volume would there be in the container when the container is 100% filled with water?
Percentage of volume of space to be filled
= 100% - 10%
= 90%
Volume of space in the container
= 90% x 120 x 50 x 49
=
90100 x 120 x 50 x 49
= 264600 cm
3 1 ℓ = 1000 mℓ
9 ℓ = 9 x 1000 = 9000 mℓ
Number of sets of 30 seconds in 1 min
= 60 ÷ 30
= 2
Water flowed in every 30 seconds
= 9000 ÷ 2
= 4500 mℓ
Total volume added for every 30 seconds
= 4500 + 200
= 4700 cm
3 Number of sets of 4700 cm
3= 264600 ÷ 4700
= 56 r 1400
After the last iron ball is added, 1400 cm
3 of water will flow into the tank so that the container is 100% filled with water.
Number of iron balls added = 56
Answer(s): 56