Question

select the correct answer
a cylindrical pressure vessel has a height of 9 feet and a diameter of 6 feet. how much gas can the pressure vessel hold when full?
a. 54π cubic feet
b. 81π cubic feet
c. 108π cubic feet
d. 324π cubic feet

Explanation:

Step1: Find the radius of the cylinder

The diameter is 6 feet, so the radius \( r=\frac{6}{2}=3 \) feet.

Step2: Recall the volume formula for a cylinder

The volume \( V \) of a cylinder is given by \( V = \pi r^{2}h \), where \( r \) is the radius and \( h \) is the height.

Step3: Substitute the values of \( r \) and \( h \)

Here, \( r = 3 \) feet and \( h = 9 \) feet. Substituting these into the formula, we get \( V=\pi\times(3)^{2}\times9 \).

Step4: Calculate the volume

First, calculate \( (3)^{2}=9 \), then multiply by 9: \( 9\times9 = 81 \). So, \( V = 81\pi \) cubic feet.

Answer:

B. 81π cubic feet