If you know the diameter D of a circular piston, which expressions correctly compute its area?

If you know the diameter D of a circular piston, which expressions correctly compute its area?

• A. Pi*r^2
• B. Pi*(D^2/4)
• C. 0.7854*D^2
• D. All of the above

Answer: (D)

Area of a circle is A = πr^2. If you know the diameter D, the radius is r = D/2, so A = π(D/2)^2 = π(D^2/4). That simplifies to (π/4)D^2, which is about 0.7854 D^2. Since these forms are all the same expression expressed differently, each one correctly computes the area when you relate the diameter to the radius. So every form is valid.

Area of a circle is A = πr^2. If you know the diameter D, the radius is r = D/2, so A = π(D/2)^2 = π(D^2/4). That simplifies to (π/4)D^2, which is about 0.7854 D^2. Since these forms are all the same expression expressed differently, each one correctly computes the area when you relate the diameter to the radius. So every form is valid.