The energy (and cost) needed to operate an air conditioner is proportional to the
volume of the space that is being cooled. It costs ZAP Electronics about $125.00
per day to run an air conditioner in its small rectangular warehouse. The company's
large warehouse, a few blocks away, is 2.5 times as long, wide, and high as the
small warehouse. Estimate the daily cost of cooling the large warehouse with the
same model of air conditioner. Round your answer to the nearest dollar.
Since the volume of the large warehouse is 2.5 times the volume of the small warehouse, we can assume that the energy (and cost) needed to cool the large warehouse will be 2.5 times the energy (and cost) needed to cool the small warehouse.
Therefore, the daily cost of cooling the large warehouse will be:
2.5 x $125.00 = $312.50
Rounded to the nearest dollar, the estimated daily cost of cooling the large warehouse with the same model of air conditioner is $313.
i thought it was $1953
I apologize for the mistake in my previous response. You are correct that the estimated daily cost of cooling the large warehouse with the same model of air conditioner is actually $1953.
To calculate this, we can use the fact that the large warehouse is 2.5 times as long, wide, and high as the small warehouse. This means its volume is:
2.5 x 2.5 x 2.5 = 15.625 times the volume of the small warehouse
So the energy (and cost) needed to cool the large warehouse is also 15.625 times the energy (and cost) needed to cool the small warehouse. Since we know that it costs $125.00 per day to cool the small warehouse, the cost to cool the large warehouse is:
15.625 x $125.00 = $1953.13
Rounded to the nearest dollar, the estimated daily cost of cooling the large warehouse with the same model of air conditioner is $1953.
i appreciate you bot
You're welcome! I'm always here to help with any questions or calculations you may have.
To estimate the daily cost of cooling the large warehouse, we need to compare the volume of the large warehouse to the small warehouse.
The volume of a rectangular space can be calculated by multiplying its length, width, and height. Since the large warehouse is 2.5 times longer, wider, and higher than the small warehouse, the volume of the large warehouse would be (2.5 × length) × (2.5 × width) × (2.5 × height).
Let's assume the length, width, and height of the small warehouse are L, W, and H, respectively. Therefore, the length, width, and height of the large warehouse would be 2.5L, 2.5W, and 2.5H, respectively.
Now, let's calculate the volume of the large warehouse:
Volume of the large warehouse = (2.5L) × (2.5W) × (2.5H)
= 15.625 × (L × W × H)
Since the energy (and cost) needed to operate the air conditioner is proportional to the volume of the space being cooled, we can write the following proportion:
Cost of cooling the small warehouse / Volume of the small warehouse = Cost of cooling the large warehouse / Volume of the large warehouse
We know that the cost of cooling the small warehouse is $125.00 per day, so we can substitute this value into the proportion:
$125.00 / (L × W × H) = Cost of cooling the large warehouse / (15.625 × L × W × H)
Now we can solve for the cost of cooling the large warehouse:
Cost of cooling the large warehouse = ($125.00 × (15.625 × L × W × H)) / (L × W × H)
= $1953.13
Rounding to the nearest dollar, the estimated daily cost of cooling the large warehouse with the same model of air conditioner is $1953.