MathsCBSE Class 10 · Basic · Board exam 2024, set 430/2/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2024: question 35(b)

Set in the CBSE Class 10 board exam of 2024, paper 430/2/1, section D, question 35(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q35(b) · 5 marks · Long answerSurface Areas and Volumes

From a solid cylinder of height 8 cm and radius 6 cm, a conical cavity of the same height and same radius is carved out. Find the total surface area of the remaining solid. (Take $π = 3.14$ )

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/2/1.

Hints

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

Hint 1

Think about which surfaces are visible after the cone is scooped out: the top circle is gone, but a new surface appears inside.

Hint 2

The inside surface is the curved surface of the cone, which needs the slant height $l = r^{2} + h^{2}$ .

Hint 3

Add: curved surface of cylinder + bottom circle + curved surface of cone.

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.

For the cone: $r = 6$ cm, $h = 8$ cm.
Slant height $l = r^{2} + h^{2} = 6^{2} + 8^{2} = 100 = 10$ cm
1 mark
The remaining solid is bounded by the curved surface of the cylinder, its uncarved circular base and the curved surface of the conical cavity.
TSA $= 2 π r h + π r^{2} + π r l = 2 π (6) (8) + π (6)^{2} + π (6) (10)$
2½ marks
$= 96 π + 36 π + 60 π = 192 π$
1 mark
$= 192 \times 3.14 = 602.88 cm^{2}$
½ mark

Answer: Total surface area of the remaining solid = 192π = 602.88 cm²

Where the marks are

Finds slant height $l = 10$ cm (1 mark)
Writes TSA $= 2 π r h + π r^{2} + π r l$ with correct substitution (2½ marks)
Simplifies to $192 π$ (1 mark)
Final value $602.88 cm^{2}$ (½ 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 paper2024 board paper, set 430/2/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2024: question 35(b)

Hints

Step-by-step solution

Revise the chapter

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