MathsCBSE Class 10 · Basic · Board exam 2024, set 430/1/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2024: question 30(A)

Set in the CBSE Class 10 board exam of 2024, paper 430/1/1, section C, question 30(A), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30(A) · 3 marks · Short answerSurface Areas and Volumes

A solid is in the form of a cylinder with hemi-spherical ends of same radii. The total height of the solid is 20 cm and the diameter of the cylinder is 14 cm. Find the surface area of the solid.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/1/1.

Hints

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

Hint 1

The total height includes the two hemispherical ends, each of height equal to the radius.

Hint 2

Add the curved surface area of the cylinder and of the two hemispheres (no flat faces are exposed).

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 of cylinder = radius of each hemisphere $= r = \frac{14}{2} = 7$ cm
½ mark
Height of cylinder $h = 20 - 2 \times 7 = 6$ cm
½ mark
Surface area = CSA of cylinder + CSA of two hemispheres $= 2 π r h + 2 (2 π r^{2}) = 2 π r (h + 2 r) = 2 \times \frac{22}{7} \times 7 \times (6 + 14) = 44 \times 20$
1½ marks
$= 880$ cm²
½ mark

Answer: 880 cm²

Where the marks are

r = 7 cm (½ mark)
Cylinder height 6 cm (½ mark)
Correct formula $2 π r h + 4 π r^{2}$ and substitution (1½ marks)
880 cm² (½ mark)

Revise the chapter

Chapter: Surface Areas and Volumes (notes, formulas, where marks are lost and every past question)
Topic: Surface Area 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 paper2024 board paper, set 430/1/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2024: question 30(A)

Hints

Step-by-step solution

Revise the chapter

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