Answer:
240.625 gallons
Step-by-step explanation:
Given:
- Height of the tank (when full) = 8 ft
- Capacity of the tank (when full) = 350 gallons
How many gallons remain in the tank when the depth of oil is 5 1/2ft?
Let's assume x represents the number of gallons remaining when the depth of oil is 5 1/2 feet.
Remaining gallons / Full capacity = Remaining height / Full height
x / 350 = 5.5 / 8
x = (5.5/8) · 350
x = 240.625 gallons
So, 240.625 gallons remain in the tank when the depth of oil is 5 1/2 feet.
A cylindrical oil tank with a depth of 5 1/2 feet holds 240.625 gallons of oil when the full capacity at 8 feet is 350 gallons.
The student has asked how many gallons remain in the cylindrical oil tank when the depth of oil is 5 1/2 feet, given that the tank holds 350 gallons when filled to its full capacity of 8 feet. To find out how many gallons are in the tank when it's partially filled, we need to calculate the volume of oil at the new depth proportionally. Since the volume of a cylinder is directly proportional to its height, we can set up a ratio comparing the two heights and the two volumes.
The volume of the tank when it is full (8 ft) is 350 gallons. Therefore, when the tank is 5.5 ft deep, the volume can be calculated as follows:
V5.5ft = (5.5 ft / 8 ft) × 350 gallons
V5.5ft = 0.6875 × 350 gallons
V5.5ft = 240.625 gallons
So, when the oil tank is at a depth of 5 1/2 feet, it contains 240.625 gallons of oil.
