Answer: The height of the cylindrical garbage can can be calculated using the formula for the volume of a cylinder:
V = πr^2h
where V is the volume of the cylinder, r is the radius (which is half of the diameter), and h is the height of the cylinder.
First, we need to convert the diameter from feet to inches, since the volume is given in cubic inches. One foot is equal to 12 inches, so 2 feet is equal to 24 inches.
The radius of the cylinder is half of the diameter, so:
r = 24/2 = 12 inches
Now we can plug in the values we have into the formula and solve for h:
50nft = π(12 inches)^2h
We can simplify this by first converting the volume from cubic feet to cubic inches. Since 1 foot is equal to 12 inches, 1 cubic foot is equal to (12 inches)^3 = 1728 cubic inches. Therefore:
50nft = 50 x 1728 cubic inches = 86400 cubic inches
Substituting this value into the formula, we get:
86400 = π(12 inches)^2h
Simplifying further:
86400 = 144πh
Dividing both sides by 144π, we get:
h = 86400 / (144π) inches
Using a calculator to evaluate this expression, we get:
h ≈ 199.08 inches
Therefore, the height of the cylindrical garbage can is approximately 199.08 inches.