MathsCBSE Class 10 · Standard · Board exam 2024, set 30/3/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2024: question 35(a)

Set in the CBSE Class 10 board exam of 2024, paper 30/3/1, section D, question 35(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q35(a) · 5 marks · Long answerCompetency-basedSurface Areas and Volumes

A solid iron pole consists of a solid cylinder of height 200 cm and base diameter 28 cm, which is surmounted by another cylinder of height 50 cm and radius 7 cm. Find the mass of the pole, given that $1 cm^{3}$ of iron has approximately 8 g mass.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/3/1.

Hints

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

Hint 1

The pole is made of two cylinders, so add their volumes.

Hint 2

Use $V = π r^{2} h$ for each cylinder. The lower radius is half of 28 cm.

Hint 3

Mass = volume × 8 g. Convert the answer to kg.

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 the lower cylinder $= \frac{28}{2} = 14$ cm, and its height is $200$ cm.
The upper cylinder has radius $7$ cm and height $50$ cm.
½ mark
Volume of the lower cylinder $= π r^{2} h = \frac{22}{7} \times 14 \times 14 \times 200 = 123200 cm^{3}$
1 mark
Volume of the upper cylinder $= \frac{22}{7} \times 7 \times 7 \times 50 = 7700 cm^{3}$
1 mark
Total volume of the pole $= 123200 + 7700 = 130900 cm^{3}$
1 mark
Mass $= 8 \times 130900$
1 mark
$= 1047200$ g $= 1047.2$ kg
½ mark

Answer: Mass of pole $= 1047200$ g $= 1047.2$ kg

Where the marks are

Takes the radius of the lower cylinder as 14 cm (½ mark)
Finds the volume of the lower cylinder (1 mark)
Finds the volume of the upper cylinder (1 mark)
Gets the total volume 130900 cm³ (1 mark)
Multiplies by 8 g per cm³ (1 mark)
Final mass 1047200 g, i.e. 1047.2 kg (½ mark)

Revise the chapter

Chapter: Surface Areas and Volumes (notes, formulas, where marks are lost and every past question)

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 30/3/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 35(a)

Hints

Step-by-step solution

Revise the chapter

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