Which equation is used to compute cylinder steam-space volume in the example?

Which equation is used to compute cylinder steam-space volume in the example?

• A. V = 2π r h
• B. V = π r^2 L
• C. V = π d^2 h
• D. V = 4/3 π r^3

Answer: (B)

The essential idea is that the volume of a right circular cylinder equals the area of its circular base times its height. For a base with radius r, the area is πr^2, and when you multiply by the cylinder’s length along its axis (often denoted L or h), you get V = πr^2L. In the steam-space example, the space is modeled as a cylinder with radius r and length L, so its volume is directly V = πr^2L. The other forms don’t fit this scenario: 2πrh gives the cylinder’s lateral surface area, not its volume; πd^2h would be π(d/2)^2h, which is not the correct volume form for a cylinder; and 4/3πr^3 is the volume of a sphere, not a cylinder.

The essential idea is that the volume of a right circular cylinder equals the area of its circular base times its height. For a base with radius r, the area is πr^2, and when you multiply by the cylinder’s length along its axis (often denoted L or h), you get V = πr^2L. In the steam-space example, the space is modeled as a cylinder with radius r and length L, so its volume is directly V = πr^2L.

The other forms don’t fit this scenario: 2πrh gives the cylinder’s lateral surface area, not its volume; πd^2h would be π(d/2)^2h, which is not the correct volume form for a cylinder; and 4/3πr^3 is the volume of a sphere, not a cylinder.