Q1. [1]
Assertion (A): If we join two hemispheres of same radius along their bases, then we get a sphere.
Reason (R): Total Surface Area of a sphere of radius $r$ is $3\pi r^2$.
Select the correct answer from the codes (A), (B), (C) and (D) given below.
- A Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- B Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- C Assertion (A) is true, but Reason (R) is false.
- D Assertion (A) is false, but Reason (R) is true.
Previously asked in CBSE board exam
2025 30/1/1 Q20
Generated by claude-sonnet-4-6 · 2026-06-15 10:33 · grounding rag
Model Answer
(C) Assertion (A) is true, but Reason (R) is false.
Assertion is correct — joining two hemispheres of the same radius along their bases gives a sphere. However, the TSA of a sphere of radius $r$ is $4\pi r^2$, not $3\pi r^2$. So Reason is false.
Explanation
- The Assertion is a basic geometric fact (two hemispheres → sphere). ✓
- The standard formula for TSA of a sphere is $4\pi r^2$. The Reason incorrectly states $3\pi r^2$ (which is the TSA of a hemisphere = $2\pi r^2 + \pi r^2 = 3\pi r^2$).
- Since A is true but R is false, the answer is (C).
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