A drum 40cm in diameter contains 88 liter of oil calculate the depth of the oil in the drum
d = diameter = 40 cm
A = Area of circle
V = Volume
h = depth
1 L = 1 dm³
1 dm = 10 cm
1 L = ( 10 cm )³
1 L = 1000 cm³
88 L = 88000 cm³
V = 88000 cm³
A = d² π / 4
V = A ∙ h
V = d² π / 4 ∙ h
88000 = 40² π / 4 ∙ h
88000 = 1600 π / 4 ∙ h
88000 = 400 π ∙ h
88000 / 400 π = h
220 / π = h
h = 220 / π
h = 70.02817496 cm
h ≈ 70 cm
Well, let's dive into this problem! If we imagine the drum as a big cup, we can start by finding the volume of the cup (drum). We know that the diameter of the drum is 40 cm, which means the radius is 20 cm (because radius = diameter/2).
Next, we can use the formula for the volume of a cylinder, which is πr²h, where π is approximately 3.14, r is the radius, and h is the height (or depth) of the oil.
We're given that the drum contains 88 liters of oil, so we need to convert that to cubic centimeters (cm³). Since 1 liter is equal to 1000 cm³, the drum holds 88,000 cm³ of oil.
Plugging these values into the formula, we can solve for h:
88,000 = 3.14 * 20² * h
Now, let's take the stage and solve for h:
h = 88,000 / (3.14 * 400)
After the act of calculations, we find that h is approximately 70.52 cm. So, the depth of the oil in the drum is approximately 70.52 cm.
Remember, though, this is just a theoretical calculation. In reality, the depth of the oil might differ slightly due to factors such as the shape of the drum and how the oil is distributed. But hey, at least we had a laugh along the way, right?
To calculate the depth of the oil in the drum, we need to find the volume of oil.
Given:
Diameter of the drum = 40 cm
Volume of oil = 88 liters
We can use the formula for the volume of a cylinder to calculate the depth:
Volume of a cylinder = π * r^2 * h
Since the diameter is given, we can calculate the radius (r) by dividing the diameter by 2:
Radius (r) = diameter / 2 = 40 cm / 2 = 20 cm
Now, we can rearrange the formula to solve for the height (h):
h = Volume / (π * r^2)
Substituting the given values:
h = 88 liters / (π * (20 cm)^2)
Now, let's calculate the depth:
h = 88 liters / (3.14159 * (20 cm)^2)
h ≈ 88 liters / (3.14159 * 400 cm^2)
h ≈ 88 liters / (1256.64 cm^2)
h ≈ 0.07 cm
Therefore, the depth of the oil in the drum is approximately 0.07 cm.
To calculate the depth of the oil in the drum, we can use the formula for the volume of a cylinder. First, let's find the radius of the drum by dividing the diameter by 2.
Radius = Diameter / 2 = 40 cm / 2 = 20 cm
Next, we can calculate the volume of the drum using the formula:
Volume = π * radius^2 * height
Since we want to find the height (depth), we rearrange the formula as follows:
Height = Volume / (π * radius^2)
Given that the volume of the drum is 88 liters, we need to convert it to cubic centimeters, as the units for radius and height are in centimeters.
1 liter = 1000 cubic centimeters
So, the volume in cubic centimeters is:
Volume = 88 liters * 1000 cubic centimeters/liter = 88000 cubic centimeters
Now, we can substitute the values into the formula to find the depth:
Height = 88000 cubic centimeters / (π * (20 cm)^2) ≈ 69.8 cm
Therefore, the depth of the oil in the drum is approximately 69.8 cm.