Inside a 4-inch pipe, adding ½ gallon raises the liquid level by what distance?

Inside a 4-inch pipe, adding ½ gallon raises the liquid level by what distance?

• A. 8 inches
• B. 9 inches
• C. 10 inches
• D. 11 inches

Answer: (B)

Raising the liquid level in a cylindrical pipe depends on how much volume you add compared to the cross-sectional area of the pipe. The height change is V/A, where V is the added volume and A is the cross-sectional area. Here, the pipe has an inside diameter of 4 inches, so the cross-sectional area is A = πr^2 = π(2 inches)^2 = 4π square inches ≈ 12.566 in^2. Adding 1/2 gallon converts to cubic inches: 0.5 × 231 = 115.5 in^3. The rise in height is h = V/A = 115.5 / 12.566 ≈ 9.2 inches. So the liquid level increases by about 9 inches, making that the closest answer.

Raising the liquid level in a cylindrical pipe depends on how much volume you add compared to the cross-sectional area of the pipe. The height change is V/A, where V is the added volume and A is the cross-sectional area.

Here, the pipe has an inside diameter of 4 inches, so the cross-sectional area is A = πr^2 = π(2 inches)^2 = 4π square inches ≈ 12.566 in^2. Adding 1/2 gallon converts to cubic inches: 0.5 × 231 = 115.5 in^3. The rise in height is h = V/A = 115.5 / 12.566 ≈ 9.2 inches. So the liquid level increases by about 9 inches, making that the closest answer.