a cylindrical drum of diameter 56 cm contains 123.2 litres of oil when full. Find the height of the drum in centimeters
Answer Details
To solve the problem, we need to use the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height of the cylinder.
We are given the diameter of the drum, which is 56 cm. To find the radius, we need to divide the diameter by 2:
radius (r) = diameter / 2 = 56 cm / 2 = 28 cm
We are also given that the drum contains 123.2 litres of oil when full. To convert litres to cubic centimeters, we need to multiply by 1000:
123.2 litres * 1000 = 123200 cubic centimeters
Now we can use the formula for the volume of a cylinder to find the height (h):
V = πr²h
h = V / (πr²)
h = 123200 / (π28²)
h ≈ 123200 / 2463.47
h ≈ 50.00 cm
Therefore, the height of the drum is approximately 50.00 cm.