What is the cross-sectional area of a piston with diameter 0.75 inches?

What is the cross-sectional area of a piston with diameter 0.75 inches?

• A. 0.4418 in^2
• B. 1.77 in^2
• C. 3.14 in^2
• D. 0.5890 in^2

Answer: (A)

The cross-sectional area of a circular piston is found with A = π r^2. Since the diameter d is twice the radius, radius = d/2, so A = π (d/2)^2 = (π/4) d^2. With d = 0.75 inches, the radius is 0.375 inches, and r^2 = 0.140625 in^2. Therefore A = π × 0.140625 ≈ 0.4418 in^2. This matches the correct value. If you accidentally use the diameter as the radius, you’d get A ≈ π × 0.75^2 ≈ 1.77 in^2, which is larger because you’re effectively treating the diameter as if it were the radius.

The cross-sectional area of a circular piston is found with A = π r^2. Since the diameter d is twice the radius, radius = d/2, so A = π (d/2)^2 = (π/4) d^2. With d = 0.75 inches, the radius is 0.375 inches, and r^2 = 0.140625 in^2. Therefore A = π × 0.140625 ≈ 0.4418 in^2. This matches the correct value.

If you accidentally use the diameter as the radius, you’d get A ≈ π × 0.75^2 ≈ 1.77 in^2, which is larger because you’re effectively treating the diameter as if it were the radius.