MathsCBSE Class 10 · Standard · Board exam 2026, set 30/3/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2026: question 25

Set in the CBSE Class 10 board exam of 2026, paper 30/3/1, section B, question 25, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25 · 2 marks · Very short answerSurface Areas and Volumes

A toy is in the form of a cone mounted on a hemisphere of radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.

Figure in the paper: A toy: a cone with vertical axis sitting on the flat circular face of a hemisphere (hemisphere below, its rim visible as an ellipse at the junction). See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/3/1.

Hints

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

Hint 1

The total height includes the hemisphere's radius. Subtract it to get the cone's height, then find the slant height.

Hint 2

Only the curved surfaces are visible. Add the cone's curved surface area and the hemisphere's curved surface area.

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.

Radius $r = 7$ cm.
Height of the cone: $h = 31 - 7 = 24$ cm.
Slant height: $l = r^{2} + h^{2} = 7^{2} + 2 4^{2} = 625 = 25$ cm.
½ mark
The flat circular faces are joined together, so they are hidden. Therefore:
TSA of toy = CSA of cone + CSA of hemisphere $= π r l + 2 π r^{2}$
$= \frac{22}{7} \times 7 \times 25 + 2 \times \frac{22}{7} \times 7 \times 7 = 550 + 308$
1 mark
$= 858$ cm².
So the total surface area of the toy is $858 cm^{2}$ .
½ mark

Answer: 858 cm²

Where the marks are

Finds the cone height 24 cm and slant height 25 cm (½ mark)
Writes TSA = $π r l + 2 π r^{2}$ and substitutes correctly (1 mark)
Gets 858 cm² (½ mark)

Revise the chapter

Chapter: Surface Areas and Volumes (notes, formulas, where marks are lost and every past question)
Topic: Cone on a Hemisphere and Similar Shapes

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 30/3/1 (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 25

Hints

Step-by-step solution

Revise the chapter

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