Case Study – 3 On a Sunday your parents took you to a fair. You could see lot of toys displayed and you wanted them to buy a Rubik's cube and a strawberry ice-cream for you. The figure shows a cube (Rubik's cube) on the left and a cone-shaped ice-cream with a hemispherical top on the right. Based on the information given above, answer the following questions : (i) Find the length of the diagonal of Rubik's cube if each edge measures 6 cm. (ii) Find the volume of Rubik's cube if the length of the edge is 7 cm. (iii)(a) What is the curved surface area of hemisphere (ice-cream) if the base radius is 7 cm? (iii)(b) If two cubes of edges 4 cm are joined end-to-end, then find the surface area of the resulting cuboid.

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/2/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2026: question 38

Set in the CBSE Class 10 board exam of 2026, paper 30/2/1, 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

Case Study – 3

On a Sunday your parents took you to a fair. You could see lot of toys displayed and you wanted them to buy a Rubik's cube and a strawberry ice-cream for you.

The figure shows a cube (Rubik's cube) on the left and a cone-shaped ice-cream with a hemispherical top on the right.

Based on the information given above, answer the following questions :

(i)
Find the length of the diagonal of Rubik's cube if each edge measures 6 cm.
1 mark
(ii)
Find the volume of Rubik's cube if the length of the edge is 7 cm.
1 mark
(iii)(a)
What is the curved surface area of hemisphere (ice-cream) if the base radius is 7 cm?
2 marks
OR
(iii)(b)
If two cubes of edges 4 cm are joined end-to-end, then find the surface area of the resulting cuboid.
2 marks

Figure in the paper: Left: a cube (Rubik's cube) drawn in perspective with dashed hidden edges. Right: an ice-cream cone with a hemispherical top shown with hatching; the hemisphere sits on top of a cone pointing downward. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/2/1.

Hints

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

Hint 1

Recall the standard formulas for a cube: its space diagonal and its volume, both in terms of the edge.

Hint 2

The curved surface of a hemisphere is half the surface of a sphere, $4 π r^{2}$ .

Hint 3

When two cubes are joined end-to-end, the length doubles while the breadth and height stay 4 cm.

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) Diagonal of a cube $= 3 \times edge = 3 \times 6 = 63$ cm (about 10.39 cm).
1 mark
(ii) Volume of a cube $= (edge)^{3} = 7^{3} = 343 cm^{3}$ .
1 mark
(iii)(a) CSA of a hemisphere $= 2 π r^{2} = 2 \times \frac{22}{7} \times 7 \times 7$ .
1 mark
(iii)(a) $= 308 cm^{2}$ .
1 mark
(iii)(b) Two cubes of edge 4 cm joined end-to-end form a cuboid with $l = 8$ cm, $b = 4$ cm, $h = 4$ cm. Surface area $= 2 (l b + bh + h l) = 2 (8 \times 4 + 4 \times 4 + 4 \times 8)$ .
1 mark
(iii)(b) $= 2 (32 + 16 + 32) = 2 \times 80 = 160 cm^{2}$ .
1 mark

Answer: (i) $63$ cm; (ii) 343 cm³; (iii)(a) 308 cm²; (iii)(b) 160 cm²

Where the marks are

(i) Uses diagonal $= 3 a$ to get $63$ cm (1 mark)
(ii) Gets volume $7^{3} = 343$ cm³ (1 mark)
(iii)(a) Writes CSA $= 2 π r^{2}$ with $r = 7$ substituted (1 mark)
(iii)(a) Gets 308 cm² (1 mark)
(iii)(b) Identifies the cuboid as 8 × 4 × 4 and applies $2 (l b + bh + h l)$ , or counts $10$ faces of $4^{2}$ (1 mark)
(iii)(b) Gets 160 cm² (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 30/2/1 (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 2026: question 38

Hints

Step-by-step solution

Revise the chapter

More questions from Surface Areas and Volumes