A wall mounted lamp, made of fabric, is shown below. Lamp has cuboidal shape, open from top and bottom. A spherical bulb of diameter 7 cm is latched with a very thin rod. (Ignore the rod while making calculations.) Dimensions of the cuboid are 24 cm × 12 cm × 17 cm. (i) Find the surface area of the bulb. (ii) What could be the maximum diameter of the bulb if at least 1 cm space is left from each side? (iii)(a) Find the area of the fabric used if there is a fold of 2 cm on top and bottom edges. (iii)(b) Find the space available inside the lamp.

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/5/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2026: question 37

Set in the CBSE Class 10 board exam of 2026, paper 30/5/1, section E, question 37, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q37 · 4 marks · Case-basedCompetency-basedSurface Areas and Volumes

A wall mounted lamp, made of fabric, is shown below. Lamp has cuboidal shape, open from top and bottom. A spherical bulb of diameter 7 cm is latched with a very thin rod. (Ignore the rod while making calculations.) Dimensions of the cuboid are 24 cm $\times$ 12 cm $\times$ 17 cm.

(i)
Find the surface area of the bulb.
1 mark
(ii)
What could be the maximum diameter of the bulb if at least 1 cm space is left from each side?
1 mark
(iii)(a)
Find the area of the fabric used if there is a fold of 2 cm on top and bottom edges.
2 marks
OR
(iii)(b)
Find the space available inside the lamp.
2 marks

Figure in the paper: Left: photograph of a fabric wall lamp with a box-shaped shade and a base fixture on a wall. Right: a cuboid drawn in perspective, labelled 24 cm (top edge length), 12 cm (depth) and 17 cm (height). Open top and bottom; a circle (the spherical bulb) is drawn at the centre of the front face with a dashed vertical line through it. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/5/1.

Hints

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

Hint 1

The surface area of a sphere is $4 π r^{2}$ ; remember that the radius is half of 7 cm.

Hint 2

For the largest bulb, look at the smallest dimension of the lamp and leave 1 cm on both sides.

Hint 3

The fabric covers only the four side faces, since the top and bottom are open. The folds add 2 cm at the top and 2 cm at the bottom to the height. For space, subtract the bulb's volume from the cuboid's volume.

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) Radius of bulb $r = \frac{7}{2}$ cm.
Surface area $= 4 π r^{2} = 4 \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} = 154$ cm².
1 mark
(ii) The bulb must fit within the smallest dimension of the lamp, 12 cm, with at least 1 cm left on each side.
Maximum diameter $= 12 - 2 \times 1 = 10$ cm.
1 mark
(iii)(a) The lamp is open at top and bottom, so only the four side faces use fabric. A 2 cm fold at the top and at the bottom increases the height to $17 + 2 + 2 = 21$ cm.
The effective dimensions are $24 cm \times 12 cm \times 21 cm$ .
1 mark
(iii)(a) Fabric area = lateral surface area $= 2 (l + b) h = 2 \times (24 + 12) \times 21 = 1512$ cm².
1 mark
(iii)(b) Space available = volume of cuboid − volume of bulb
$= 24 \times 12 \times 17 - \frac{4}{3} \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times \frac{7}{2}$
1 mark
(iii)(b) $= 4896 - \frac{539}{3} = \frac{14688 - 539}{3} = \frac{14149}{3}$ cm³ $\approx 4716.33$ cm³
1 mark

Answer: (i) 154 cm²; (ii) 10 cm; (iii)(a) 1512 cm²; (iii)(b) 14149/3 cm³ ≈ 4716.33 cm³

Where the marks are

(i) Surface area of bulb = 4πr² = 154 cm² (1 mark)
(ii) Maximum diameter = 12 − 2 = 10 cm (1 mark)
(iii)(a) Height with folds = 21 cm, so dimensions 24 × 12 × 21 (1 mark)
(iii)(a) Fabric area = 2 × 21 × (24 + 12) = 1512 cm² (1 mark)
(iii)(b) Writes volume of cuboid minus volume of sphere with correct values (1 mark)
(iii)(b) Space = 14149/3 cm³ ≈ 4716.3 cm³ (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 paper2026 board paper, set 30/5/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 37

Hints

Step-by-step solution

Revise the chapter

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