Steve pored six 2 liter bottles of apple juice into an empty rectangular drink dispenser measuring 40 centimeters long and 20 centimeters wide. Calculate the interior area of the dispenser that is in contact with the apple juice. 1 L is 1000cm3
20 cm
To calculate the interior area of the dispenser in contact with the apple juice, we need to determine the volume of the apple juice and then find the corresponding area.
First, let's calculate the total volume of the apple juice poured into the dispenser. Since each bottle is a 2-liter bottle, the total volume is 2 liters x 6 bottles = 12 liters.
Given that 1 L is equal to 1000 cm^3, we can convert the volume to cubic centimeters by multiplying 12 liters x 1000 cm^3/liter = 12,000 cm^3.
Now, let's find the corresponding area in contact with the apple juice. To do this, we need to determine the height of the liquid. Since the dispenser is rectangular, the height can be calculated by dividing the volume by the base area, which is the product of length and width.
The base area is 40 cm x 20 cm = 800 cm^2.
The height can be calculated by dividing the volume (12,000 cm^3) by the base area (800 cm^2), resulting in a height of 15 cm.
Finally, the interior area in contact with the apple juice is equal to the base area (800 cm^2) multiplied by the height (15 cm), which gives us 12,000 cm^2.