MathsCBSE Class 10 · Basic · Board exam 2026, set 430/4/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Basic 2026: question 38

Set in the CBSE Class 10 board exam of 2026, paper 430/4/1, section E, question 38, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q38 · 4 marks · Case-basedCompetency-basedSurface Areas and Volumes

'Gilli Danda' is a very popular traditional game of India which is played with two wooden sticks – the larger one is called 'Danda' and smaller one 'Gilli'.

'Danda' – It is cylindrical in shape with diameter $4$ cm and length $42$ cm.

Gilli – It is cylindrical in middle with identical conical ends of same radius $1.5$ cm and length $2.8$ cm. The length of cylindrical part is $7$ cm.

Based on the above, answer the following questions :

(i)
Find the volume of wood used in making both the conical parts of Gilli.
1 mark
(ii)
Find the volume of wood used in making cylindrical part of Gilli.
1 mark
(iii)
(a) A cylindrical log of wood of radius $1.5$ cm and length $14$ cm is used to make Gilli. Find the volume of the wood scrapped.
2 marks
OR
(iii)
(b) Find the total surface area of 'Danda'.
2 marks

Figure in the paper: Left: a long cylindrical stick (Danda) and a short stick (Gilli). Right: Danda is a long cylinder with diameter 4 cm and length 42 cm. Gilli is a cylinder of length 7 cm with a cone attached at each end; the cones have radius 1.5 cm and slant/height dimension 2.8 cm marked. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/4/1.

Hints

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

Hint 1

The Gilli is made of one cylinder and two identical cones; find each volume separately.

Hint 2

Cone volume is $\frac{1}{3} π r^{2} h$ and cylinder volume is $π r^{2} h$ . The wood scrapped is the log's volume minus the Gilli's volume.

Hint 3

For the Danda, halve the diameter to get the radius, then use TSA $= 2 π r (r + h)$ .

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.

(i) Each cone has $r = 1.5$ cm and $h = 2.8$ cm.
Volume of both cones $= 2 \times \frac{1}{3} π r^{2} h = 2 \times \frac{1}{3} \times \frac{22}{7} \times 1.5 \times 1.5 \times 2.8$
½ mark
$= \frac{2}{3} \times 19.8 = 13.2$ cm³
½ mark
(ii) The cylindrical part has $r = 1.5$ cm and $h = 7$ cm.
Volume $= π r^{2} h = \frac{22}{7} \times 1.5 \times 1.5 \times 7$
½ mark
$= 49.5$ cm³
½ mark
(iii)(a) Volume of the log $= π r^{2} h = \frac{22}{7} \times 1.5 \times 1.5 \times 14 = 99$ cm³
1 mark
Volume of the Gilli $= 13.2 + 49.5 = 62.7$ cm³
½ mark
Volume of wood scrapped $= 99 - 62.7 = 36.3$ cm³
½ mark
(iii)(b) The Danda has $r = \frac{4}{2} = 2$ cm and $h = 42$ cm.
TSA of a cylinder $= 2 π r^{2} + 2 π r h = 2 \times \frac{22}{7} \times 2 \times 2 + 2 \times \frac{22}{7} \times 2 \times 42$
1 mark
$= \frac{88}{7} \times (2 + 42) = \frac{3872}{7}$ cm² $\approx 553.14$ cm²
1 mark

Answer: (i) 13.2 cm³; (ii) 49.5 cm³; (iii)(a) 36.3 cm³; (iii)(b) $\frac{3872}{7}$ cm² ≈ 553.14 cm²

Where the marks are

Applies $2 \times \frac{1}{3} π r^{2} h$ with $r = 1.5$ , $h = 2.8$ (½ mark) and gets 13.2 cm³ (½ mark)
Applies $π r^{2} h$ with $h = 7$ (½ mark) and gets 49.5 cm³ (½ mark)
Finds the volume of the log as 99 cm³ (1 mark)
Finds the volume of the Gilli as 62.7 cm³ (½ mark)
Finds the wood scrapped as 36.3 cm³ (½ mark)
Uses TSA $= 2 π r^{2} + 2 π r h$ with $r = 2$ , $h = 42$ (1 mark)
Gets $\frac{3872}{7}$ cm² ≈ 553.14 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 paper2026 board paper, set 430/4/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2026: question 38

Hints

Step-by-step solution

Revise the chapter

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