Water is poured steadily into an empty container. If the volume of water in the
container after 5 seconds is 30 cm3 , find
a) The rate of change of volume
b) The volume of water after 12 seconds
rate of change of volume = change in volume / change in time
= (30-0)/(5-0) = 6 cm^3 /second
so if it fulls up at 6 cm^3 in 1 second , how much will there be in 12 seconds ?
15
To find the rate of change of volume, we need to calculate the change in volume per unit time. In this case, the change in volume is given as 30 cm³ after 5 seconds.
a) The rate of change of volume:
To find the rate of change, we divide the change in volume by the time taken. So, the rate of change of volume is:
Rate of change of volume = Change in volume / Time taken
Rate of change of volume = 30 cm³ / 5 seconds = 6 cm³/s
Therefore, the rate of change of volume is 6 cm³/s.
b) To find the volume of water after 12 seconds, we can use the rate of change of volume we calculated above. Since the rate of change is constant, we can use it to find the volume at any given time.
Volume after 12 seconds = Volume after 5 seconds + (Rate of change of volume × Time difference)
Volume after 12 seconds = 30 cm³ + (6 cm³/s × 12 seconds)
Volume after 12 seconds = 30 cm³ + 72 cm³
Volume after 12 seconds = 102 cm³
Therefore, the volume of water after 12 seconds is 102 cm³.