The Blackbird Oil Company is considering the purchase of 20new jumbo oil storage tanks. The standard model holds 12,000 gallons. Its dimensions are 4/5 the size of the similarly shaped jumbo model, that is, the ratio of the dimensions is 4:5
so, the new tanks will hold (5/4)^3 as much oil, or 23437.5 gallons each
why did you make this question now its in my geometry class
To find out the capacity of the jumbo model, we need to set up a proportion using the dimensions ratio.
Let's assume the dimensions of the jumbo model are:
Length = L
Width = W
Height = H
Based on the given information, the dimensions of the standard model are:
Length = 4L/5
Width = 4W/5
Height = 4H/5
The capacity of a tank is calculated by multiplying its dimensions together. So, the capacity of the standard model is:
Standard Capacity = (4L/5) * (4W/5) * (4H/5) = (64LWH) / (125)
Since we know that the capacity of the standard model is 12,000 gallons, we can set up the following proportion:
Standard Capacity / 12,000 = Jumbo Capacity / (20 * Standard Capacity)
Now, we can solve for Jumbo Capacity:
12,000 * (20 * Standard Capacity) = Standard Capacity * Jumbo Capacity
240,000 * Standard Capacity = Standard Capacity * Jumbo Capacity
Jumbo Capacity = 240,000 gallons
Therefore, the jumbo model's capacity is 240,000 gallons.
To find the dimensions of the jumbo oil storage tank, we need to use the given information that the standard model holds 12,000 gallons and its dimensions are 4/5 the size of the jumbo model.
Step 1: Determine the dimensions of the standard model.
Since the standard model holds 12,000 gallons, its dimensions are unknown. Let's call the length, width, and height of the standard model as Ls, Ws, and Hs, respectively.
Step 2: Calculate the dimensions of the jumbo model.
Given that the dimensions of the standard model are 4/5 the size of the jumbo model, we can write the ratio as follows:
Ls: Lj = 4:5
Ws: Wj = 4:5
Hs: Hj = 4:5
To calculate the dimensions of the jumbo model, we need to multiply the dimensions of the standard model by the reciprocals of their respective ratios:
Lj = Ls * (5/4)
Wj = Ws * (5/4)
Hj = Hs * (5/4)
Step 3: Consider the dimensions of the jumbo oil storage tanks.
Since we know the dimensions of the jumbo model, we can calculate the capacity of the jumbo oil storage tanks.
Capacity of one jumbo oil storage tank = Lj * Wj * Hj
Total capacity of 20 new jumbo oil storage tanks = 20 * Capacity of one jumbo oil storage tank
By following these steps, we can determine the dimensions of the jumbo oil storage tanks and calculate their total capacity.