A rectangular tank has a base of 25 cm by 20 cm and contains water to a depth of 10 cm. A solid metal cube of edge 10 cm is then placed in the tank and is fully submerged. Find the new depth of the water in the tank. (Assume the water does not overflow.)
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Worked Solution
Step 1: Volume of water originally in tank = 25 × 20 × 10 = 5000 cm³.
Step 2: Volume of cube = 10 × 10 × 10 = 1000 cm³.
Step 3: When the cube is submerged, the water level rises so that water + submerged cube together fill the tank up to the new line: Total volume below water line = 5000 + 1000 = 6000 cm³.
Step 4: New depth = total volume ÷ base area = 6000 ÷ (25 × 20) = 6000 ÷ 500 = 12 cm. (Cube top at 10 cm sits below new water line at 12 cm — fully submerged.) ✓
Answer: 12 cm
Correct answer: 12 cm
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