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 3π r². (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.

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/1/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard 2025: question 20

Set in the CBSE Class 10 board exam of 2025, paper 30/1/1, section A, question 20, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q20 · 1 mark · Assertion-reasonCompetency-basedSurface Areas and Volumes

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 $3 π r^{2}$ .

(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.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/1/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Picture joining two half-balls along their flat faces.

Hint 2

Recall the surface area of a sphere. Is it $3 π r^{2}$ ?

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Two equal hemispheres joined along their circular bases form a complete sphere. Assertion (A) is true.
The surface area of a sphere is $4 π r^{2}$ , not $3 π r^{2}$ ( $3 π r^{2}$ is the TSA of a solid hemisphere). So Reason (R) is false, and the answer is option (C).
1 mark

Answer: Option (C)

Where the marks are

States that A is true and R is false (sphere's area is $4 π r^{2}$ ), option (C) (1 mark)

Revise the chapter

Chapter: Surface Areas and Volumes (notes, formulas, where marks are lost and every past question)
Topic: Surface Area and Volume Formulae Revision

Practise this chapterBoard-style questions from Surface Areas and Volumes, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 30/1/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 20

Hints

Step-by-step solution

Revise the chapter

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