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DIRECTION: In the… (Class 10 Maths SQP 2023-24, Q19)

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MathsCBSE Class 10 · Standard · Sample paper, session 2023-24 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard sample paper 2023-24: question 19

From the official CBSE sample question paper for 2023-24, section A, question 19, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q19 · 1 mark · Assertion-reasonCompetency-basedSurface Areas and Volumes

DIRECTION: In the question number 19 and 20, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct option.

Statement A (Assertion): Total Surface area of the top is the sum of the curved surface area of the hemisphere and the curved surface area of the cone.

Statement R (Reason): Top is obtained by joining the plane surfaces of the hemisphere and cone together.

  1. (A)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
  2. (B)Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)
  3. (C)Assertion (A) is true but reason (R) is false.
  4. (D)Assertion (A) is false but reason (R) is true.

Figure in the paper: A top (toy-like solid) made of a hemisphere on top of a cone, with the flat circular face of the hemisphere joined to the circular base of the cone; the cone point faces downward. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

Which surfaces of the top can you actually see?

Hint 2

Joining the flat faces hides them.

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.

  1. The top is formed by joining the flat face of the hemisphere to the base of the cone, so these plane faces are hidden. R is true.

  2. Only the curved surfaces stay exposed, so TSA = CSA of hemisphere + CSA of cone. A is true, and R explains why. Option (A).

    1 mark

Answer: Option (A)

Where the marks are

  • Recognises both statements are true and R explains A, option (A) (1 mark)

Revise the chapter

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 paperSample paper 2023-24 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.