Final answer:
To calculate the total volume of sand needed for three sandboxes, the proportionality constant is first determined from given values and then used to find the volume at the new height. The total volume needed is 840 in³.
Step-by-step explanation:
The question involves finding the total volume of sand required for three sandboxes at a playground, given that the height of sand is proportional to the volume of the sandbox. It is provided that when the height of the sand is 2.25 in, the volume of the sand is 180 in³. To find the volume of sand in each sandbox at a new height of 3.5 in, we'll use the concept of proportionality.
First, we calculate the proportionality constant using the formula volume of sand = proportionality constant × height of sand. With the known values, this gives us a proportionality constant of 180 in³ / 2.25 in = 80 in².
Next, we use this constant to find the new volume for a height of 3.5 in: Volume of sand at 3.5 in = 80 in² × 3.5 in = 280 in³ for one sandbox. For three sandboxes, total volume = 3 × 280 in³ = 840 in³.