Assertion (A): For identical mix, the cube compressive strength of concrete obtained from 15 cm cube is higher than 15×30 cm cylinder compressive strength. Reason (R): Cube compressive strength is higher than the cylinder compressive strength because of its higher contact area under the load.
- ABoth A & R are true and R is the correct explanation of A
- BBoth A & R are true but R is not the correct explanation of A
- CA is true but R is falseCorrect
- DA is false but R is true
Solution
Concept
Cube vs Cylinder Compressive Strength of Concrete
Formula
No formula
Step-by-step solution
1. Evaluate Assertion (A): The cube strength of concrete is higher than the cylinder strength for the same mix (typically cube strength ≈ 1.25 × cylinder strength), so Assertion (A) is true. 2. Evaluate Reason (R): The higher strength in cubes is due to greater platen restraint (smaller height-to-width ratio), not contact area, so Reason (R) is false. 3. Select Option C: Assertion (A) is true but Reason (R) is false.
Explanation
Option C is correct because Assertion (A) is true while Reason (R) is false. A cube specimen gives a higher tested compressive strength than a cylinder because its smaller height-to-width ratio creates greater friction and end-restraint from the testing machine's platens across the sample. It is not due to having a larger contact area.
Shortcut
Remember the key rule: "Shorter Specimen = Greater Restraint = Higher Strength". - Fact: Cube height-to-width ratio is 1:1, whereas Cylinder is 2:1. Shorter specimens experience greater end-restraint (friction) from testing machine platens, making the Cube stronger (Cube Strength ≈ 1.25 × Cylinder Strength). - Trick for Reason: Always attribute the higher strength of cubes to "platen restraint / height-to-width ratio", never to "contact area".
Common mistake
Many students mistakenly believe that Reason (R) is true by assuming higher cube strength is due to a larger contact area, rather than the lower height-to-width ratio and platen restraint (end friction restraint). Consequently, they incorrectly select Option A or Option B instead of Option C.
Correct answer: C) A is true but R is false