Hydrostatic force on submerged vertical face Steps:

• Block Y is a rectangular prism with base a × 2a and height 2a; shaded face is vertical 2a × 2a = 4a² area, top at liquid surface, fully submerged to depth 2a.
• Liquid density ρ/2; pressure at depth h is (ρ/2)gh.
• Centroid of face at depth a from surface; average pressure = (ρ/2)ga.
• Thrust = average pressure × area = (ρ/2)ga × 4a² = 2ρa³ (g omitted).

Why C is correct:

• Matches formula for total hydrostatic force on vertical surface: density × g × centroid depth × area.

Why the others are wrong:

• A: Underestimates by factor of 2, as if density ρ but area 2a².
• B: U is undefined or irrelevant distractor, not a force value.
• D: Overestimates by factor of 2, as if full bottom pressure ρg(2a) × 2a².

Final answer: C