Answer: To calculate the volume of the gas that the cylindrical pressure vessel can hold when it is full, we can use the formula for the volume of a cylinder:
Volume = π * r^2 * h
where:
π is the mathematical constant pi (approximately 3.14159)
r is the radius of the cylinder (which is half of the diameter)
h is the height of the cylinder
Given information:
Height (h) = 9 feet
Diameter = 6 feet
First, we need to find the radius (r) using the formula for the diameter:
Diameter = 2 * r
6 feet = 2 * r
r = 6 feet / 2
r = 3 feet
Now, we have the height (h = 9 feet) and the radius (r = 3 feet). We can plug these values into the volume formula:
Volume = π * (3 feet)^2 * 9 feet
Volume = π * 9 feet^2 * 9 feet
Volume = 81π cubic feet
Now, approximate the value of π to get the final answer:
Volume ≈ 81 * 3.14159 cubic feet
Volume ≈ 254.47 cubic feet
So, the cylindrical pressure vessel can hold approximately 254.47 cubic feet of gas when it is full.