MathsCBSE Class 10 · Basic · Board exam 2026, set 430/4/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2026: question 3

Set in the CBSE Class 10 board exam of 2026, paper 430/4/1, section A, question 3, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q3 · 1 mark · MCQSurface Areas and Volumes

Two wooden solid hemispheres of same radii $r$ , are joined at a point, as shown in the figure. The total surface area of the object is :

(A) $4 π r^{2}$
(B) $6 π r^{2}$
(C) $3 π r^{2}$
(D) $5 π r^{2}$

Figure in the paper: Two solid hemispheres of equal radius r joined at their flat faces' rims to a common point, one hemisphere above the other, with the curved surfaces facing outward (a bowl-shaped top and bottom, meeting at a point). 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

Is any surface hidden when the solids meet at only a point?

Hint 2

Find the TSA of one solid hemisphere first.

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.

The hemispheres touch only at a point, so no surface is hidden. Each hemisphere shows its curved surface $2 π r^{2}$ and its flat face $π r^{2}$ , a total of $3 π r^{2}$ .
Total surface area $= 2 \times 3 π r^{2} = 6 π r^{2}$ , so option (B).
1 mark

Answer: $6 π r^{2}$ , option (B)

Where the marks are

Adds the full TSA of both hemispheres to get $6 π r^{2}$ (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 430/4/1 (Basic): 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 Basic 2026: question 3

Hints

Step-by-step solution

Revise the chapter

More questions from Surface Areas and Volumes