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.
Please help I have no idea how to do this ;-; (or even what it's asking really)
the volume of the large warehouse is 2.5^3 times the volume of the small one
daily cooling cost is ... $125.00 * (2.5^3)
Oh alright! Thank you!
Well, let me break it down for you! Air conditioners use energy to cool a given space, and the energy/cost needed is directly proportional to the volume of that space. In this case, ZAP Electronics has a small rectangular warehouse and a larger one nearby.
The dimensions of the large warehouse are given as 2.5 times the length, width, and height of the small warehouse. This means that the large warehouse is 2.5 * length, 2.5 * width, and 2.5 * height.
To estimate the cost of cooling the large warehouse, we need to compare the volumes of the two warehouses. The volume of a rectangular space is calculated by multiplying its length, width, and height.
Let's assume the small warehouse has dimensions L, W, and H.
The volume of the small warehouse is L * W * H.
The volume of the large warehouse would be (2.5 * L) * (2.5 * W) * (2.5 * H).
Since the energy/cost is directly proportional to volume, we can set up a ratio:
(volume of the large warehouse) / (volume of the small warehouse) = (cost of cooling the large warehouse) / (cost of cooling the small warehouse).
Substituting the volumes into the ratio:
((2.5 * L) * (2.5 * W) * (2.5 * H)) / (L * W * H) = (cost of cooling the large warehouse) / ($125.00).
Simplifying the ratio:
(2.5^3) * (L * W * H) / (L * W * H) = (cost of cooling the large warehouse) / ($125.00).
Canceling out the common terms:
2.5^3 = (cost of cooling the large warehouse) / ($125.00).
Now we can find the cost of cooling the large warehouse:
(cost of cooling the large warehouse) = (2.5^3) * ($125.00).
Calculating:
(cost of cooling the large warehouse) = 15.625 * ($125.00).
Rounding to the nearest dollar:
(cost of cooling the large warehouse) ≈ $1953.13.
So, it would cost approximately $1,953 per day to cool the large warehouse with the same model of air conditioner.
I hope that helps! If not, at least I tried to make math a little funny!
To estimate the daily cost of cooling the large warehouse, we need to compare the volumes of the small and large warehouses. Since the cost is proportional to the volume, the ratio of the volume of the large warehouse to the volume of the small warehouse will give us the ratio of the costs.
Let's break down the problem step-by-step:
Step 1: Calculate the volume of the small warehouse.
Given that the small warehouse is rectangular, let's call its length, width, and height as L, W, and H, respectively. As the problem doesn't provide these values, let's assume some values for the sake of calculation. Let's say L = 10 feet, W = 8 feet, and H = 6 feet.
The volume of the small warehouse is given by:
Volume_small = L x W x H
Using the assumed values:
Volume_small = 10 ft x 8 ft x 6 ft = 480 ft³
Step 2: Calculate the volume of the large warehouse.
Since the large warehouse is 2.5 times as long, wide, and high as the small warehouse, we can calculate its volume using these ratios.
Let's denote the length, width, and height of the large warehouse as 2.5L, 2.5W, and 2.5H, respectively.
The volume of the large warehouse is given by:
Volume_large = (2.5L) x (2.5W) x (2.5H)
Substituting the actual values:
Volume_large = (2.5 x 10 ft) x (2.5 x 8 ft) x (2.5 x 6 ft)
Volume_large = 625 ft³ x 400 ft³ x 1500 ft³
Volume_large = 1500000 ft³
Step 3: Calculate the ratio of the volumes.
The ratio of the volumes is given by:
Volume_ratio = Volume_large / Volume_small
Using the calculated values:
Volume_ratio = 1500000 ft³ / 480 ft³
Volume_ratio ≈ 3125
Step 4: Calculate the daily cost of cooling the large warehouse.
The cost of cooling the large warehouse can be estimated by multiplying the volume ratio by the daily cost of cooling the small warehouse.
Cost_large ≈ Volume_ratio * Cost_small
Cost_large ≈ 3125 * $125.00
Calculating the result:
Cost_large ≈ $390,625
Therefore, the estimated daily cost of cooling the large warehouse is approximately $390,625.
No problem! This problem is asking you to estimate the daily cost of cooling the large warehouse, based on the information given about the small warehouse.
First, let's understand the given information. It is mentioned that the energy (and cost) needed to operate an air conditioner is proportional to the volume of the space that is being cooled. In simpler terms, the larger the space, the more energy and cost is required to cool it.
The problem provides the cost to run the air conditioner in the small rectangular warehouse, which is $125.00 per day. It also tells us that the large warehouse is 2.5 times as long, wide, and high as the small warehouse.
To estimate the daily cost of cooling the large warehouse, we need to compare the volumes of the small and large warehouses. Since the volumes are proportional to the energy and cost, we can use the ratio of volumes to find the ratio of costs.
The volume of a rectangular warehouse is calculated by multiplying its length, width, and height. Let's assume that the length, width, and height of the small warehouse are 'L', 'W', and 'H' respectively. Therefore, the volume of the small warehouse is given by V(small) = L * W * H.
Based on the given information, the dimensions of the large warehouse are 2.5 times those of the small warehouse. Therefore, the dimensions of the large warehouse are 2.5L, 2.5W, and 2.5H respectively. Hence, the volume of the large warehouse is V(large) = (2.5L) * (2.5W) * (2.5H).
Next, we need to find the ratio of volumes: V(large) / V(small). Substitute the respective values to calculate the ratio.
(V(large) / V(small)) = ((2.5L) * (2.5W) * (2.5H)) / (L * W * H)
Simplifying this equation, we get:
(V(large) / V(small)) = 2.5 * 2.5 * 2.5 = 15.625
This means that the volume of the large warehouse is approximately 15.625 times the volume of the small warehouse.
Now, using the proportionality mentioned earlier, we can find the estimated daily cost of cooling the large warehouse. Multiply the daily cost of cooling the small warehouse ($125.00) by the volume ratio we found earlier:
Estimated cost of cooling the large warehouse = $125.00 * 15.625
Estimated cost = $1,953.125
Finally, rounding the estimated cost to the nearest dollar, we get: $1,953.
Therefore, it is estimated that it will cost approximately $1,953 per day to cool the large warehouse with the same model of air conditioner.