MathsCBSE Class 10 · Basic · Board exam 2023, set 430/2/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2023: question 11

Set in the CBSE Class 10 board exam of 2023, paper 430/2/1, section A, question 11, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q11 · 1 mark · MCQSurface Areas and Volumes

A solid is of the form of a cone of radius 'r' surmounted on a hemisphere of the same radius. If the height of the cone is the same as the diameter of its base, then the volume of the solid is:

(A) $π r^{3}$
(B) $\frac{4}{3} π r^{3}$
(C) $3 π r^{3}$
(D) $\frac{2}{3} π r^{3}$

Figure in the paper: A cone with its base circle of radius r resting on the flat face of a hemisphere of the same radius r; the radius r is marked from the centre of the base to its edge. The cone's apex is directly above the centre. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/2/1.

Hints

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

Hint 1

Height of cone = diameter = 2r.

Hint 2

Add the cone and hemisphere volumes.

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.

Cone height $h = 2 r$ , so cone volume $= \frac{1}{3} π r^{2} (2 r) = \frac{2}{3} π r^{3}$ ; hemisphere volume $= \frac{2}{3} π r^{3}$ .
Total $= \frac{2}{3} π r^{3} + \frac{2}{3} π r^{3} = \frac{4}{3} π r^{3}$ . Option (B).
1 mark

Answer: $\frac{4}{3} π r^{3}$ , option (B)

Where the marks are

Adds cone ( $h = 2 r$ ) and hemisphere volumes to get $\frac{4}{3} π r^{3}$ (1 mark)

Revise the chapter

Chapter: Surface Areas and Volumes (notes, formulas, where marks are lost and every past question)
Topic: Volume of a Combination of Solids

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 paper2023 board paper, set 430/2/1 (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 2023: question 11

Hints

Step-by-step solution

Revise the chapter

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