The volume of a solid hemisphere is 396/7\ cm³. The total surface area of the solid hemisphere (in sq.cm) is (A) 396/7 (B) 594/7 (C) 549/7 (D) 604/7

MathsCBSE Class 10 · Standard · Sample paper, session 2024-25 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard sample paper 2024-25: question 13

From the official CBSE sample question paper for 2024-25, section A, question 13, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q13 · 1 mark · MCQSurface Areas and Volumes

The volume of a solid hemisphere is $\frac{396}{7} c m^{3}$ . The total surface area of the solid hemisphere (in sq.cm) is

(A) $\frac{396}{7}$
(B) $\frac{594}{7}$
(C) $\frac{549}{7}$
(D) $\frac{604}{7}$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

Use the volume of a hemisphere, $\frac{2}{3} π r^{3}$ , to find $r$ .

Hint 2

The total surface area of a solid hemisphere is $3 π r^{2}$ .

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.

$\frac{2}{3} \cdot \frac{22}{7} r^{3} = \frac{396}{7}$ gives $r^{3} = \frac{396 \times 3}{44} = 27$ , so $r = 3$ cm.
TSA $= 3 π r^{2} = 3 \times \frac{22}{7} \times 9 = \frac{594}{7}$ cm². The answer is option (B).
1 mark

Answer: $\frac{594}{7}$ sq cm, option (B)

Where the marks are

Finds $r = 3$ cm and TSA $= 3 π r^{2} = \frac{594}{7}$ 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 paperSample paper 2024-25 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard sample paper 2024-25: question 13

Hints

Step-by-step solution

Revise the chapter

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