99l of oil is poured into a cylindrical drum 69cm in diameter. How deep is the oil in the drum?
First, we need to find the volume of the cylinder:
V = πr²h
r = 69/2 = 34.5 cm
V = π(34.5)²h
V = 39507.75h
Next, we need to convert the volume of oil from liters to cubic centimeters:
99 liters = 99000 cubic centimeters
Now we can set up an equation to solve for h:
39507.75h = 99000
h = 99000/39507.75
h = 2.5 cm
Therefore, the oil is 2.5 cm deep in the drum.
To find the depth of the oil in the drum, we can use the formula for the volume of a cylinder:
Volume = π * r^2 * h
Where:
- Volume is the amount of oil poured (99 liters or 99,000 cm^3)
- π is a constant approximately equal to 3.14159
- r is the radius of the drum (half of the diameter, which is 69 cm / 2 = 34.5 cm)
- h is the depth of the oil
Substituting the given values into the formula:
99,000 = 3.14159 * (34.5^2) * h
Simplifying:
99,000 = 3.14159 * 1,187.025 * h
Dividing both sides by (3.14159 * 1,187.025):
99,000 / (3.14159 * 1,187.025) = h
Calculating this expression:
h ≈ 8.552 cm
Therefore, the oil in the drum is approximately 8.552 cm deep.