MathsCBSE Class 10 · Standard · Board exam 2025, set 30/5/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2025: question 34(b)

Set in the CBSE Class 10 board exam of 2025, paper 30/5/1, section D, question 34(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q34(b) · 5 marks · Long answerSurface Areas and Volumes

From a solid cylinder of height 24 cm and radius 5 cm, two cones of height 12 cm and radius 5 cm are hollowed out. Find the volume and surface area of the remaining solid.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/5/1.

Hints

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

Hint 1

Each cone is 12 cm high, so the two cones together use the full 24 cm height, one from each end.

Hint 2

Volume left = cylinder volume minus the two cone volumes.

Hint 3

For the surface, the circular ends are gone; the outside curved surface and the two cone surfaces (use the slant height) remain.

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.

Volume of remaining solid = volume of cylinder − volume of 2 cones $= \frac{22}{7} \times 5 \times 5 \times 24 - 2 \times \frac{1}{3} \times \frac{22}{7} \times 5 \times 5 \times 12 = \frac{13200}{7} - \frac{4400}{7}$
1 mark
$= \frac{8800}{7} \approx 1257.14 cm^{3}$
1 mark
Slant height of each cone: $l = 1 2^{2} + 5^{2} = 169 = 13$ cm
1 mark
The two cones are hollowed from the two ends, so both flat ends are removed. Surface area = CSA of cylinder + CSA of 2 cones $= 2 \times \frac{22}{7} \times 5 \times 24 + 2 \times \frac{22}{7} \times 5 \times 13 = \frac{5280}{7} + \frac{2860}{7}$
1 mark
$= \frac{8140}{7} \approx 1162.86 cm^{2}$
1 mark

Answer: Volume = $\frac{8800}{7} \approx 1257.14$ cm³; surface area = $\frac{8140}{7} \approx 1162.86$ cm²

Where the marks are

Correct volume expression: cylinder − 2 cones (1 mark)
Volume $= \frac{8800}{7}$ cm³ (1 mark)
Slant height l = 13 cm (1 mark)
Surface area expression: CSA of cylinder + CSA of 2 cones (1 mark)
Surface area $= \frac{8140}{7}$ cm² (1 mark)

Revise the chapter

Chapter: Surface Areas and Volumes (notes, formulas, where marks are lost and every past question)

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 30/5/1 (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.

CBSE Class 10 Mathematics Standard 2025: question 34(b)

Hints

Step-by-step solution

Revise the chapter

More questions from Surface Areas and Volumes