In a cylinder with a bore of 12 inches and a stroke of 28 inches, if the steam space is 5/8 of full travel, what is the steam-space volume in cubic inches?

In a cylinder with a bore of 12 inches and a stroke of 28 inches, if the steam space is 5/8 of full travel, what is the steam-space volume in cubic inches?

• A. 3165
• B. 2100
• C. 1978
• D. 1500

Answer: (C)

Think of steam-space volume as a portion of the cylinder’s displacement determined by how far the piston travels. The bore gives the cylinder diameter, so the cross-sectional area is A = πr^2. With a 12-inch bore, the radius is 6 inches, so A = 36π square inches. The piston’s full travel (stroke) is 28 inches, so the full volume swept in one stroke is V_full = A × stroke = 36π × 28 = 1008π cubic inches (about 3166.7 in^3). The steam space is 5/8 of that full travel, so V_steam = (5/8) × V_full = (5/8) × 1008π = 630π cubic inches. Numerically, 630π ≈ 1979.2 in^3. If you use π ≈ 3.14, you get about 1978 in^3, which matches the given option. So the steam-space volume is about 1978 cubic inches.

Think of steam-space volume as a portion of the cylinder’s displacement determined by how far the piston travels. The bore gives the cylinder diameter, so the cross-sectional area is A = πr^2. With a 12-inch bore, the radius is 6 inches, so A = 36π square inches.

The piston’s full travel (stroke) is 28 inches, so the full volume swept in one stroke is V_full = A × stroke = 36π × 28 = 1008π cubic inches (about 3166.7 in^3).

The steam space is 5/8 of that full travel, so V_steam = (5/8) × V_full = (5/8) × 1008π = 630π cubic inches. Numerically, 630π ≈ 1979.2 in^3. If you use π ≈ 3.14, you get about 1978 in^3, which matches the given option. So the steam-space volume is about 1978 cubic inches.