MathsCBSE Class 10 · Standard · Board exam 2024, set 30/2/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2024: question 37

Set in the CBSE Class 10 board exam of 2024, paper 30/2/1, section E, question 37, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q37 · 4 marks · Case-basedCompetency-basedSurface Areas and Volumes

The word 'circus' has the same root as 'circle'. In a closed circular area, various entertainment acts including human skill and animal training are presented before the crowd.

A circus tent is cylindrical upto a height of $8$ m and conical above it. The diameter of the base is $28$ m and total height of tent is $18.5$ m.

Based on the above, answer the following questions:

(i)
Find slant height of the conical part.
1 mark
(ii)
Determine the floor area of the tent.
1 mark
(iii)
(a) Find area of the cloth used for making tent.
2 marks
OR
(iii)
(b) Find total volume of air inside an empty tent.
2 marks

Figure in the paper: Photograph of a circus tent. The lower part is a cylinder with vertical striped canvas walls, and the upper part is a conical roof with a pointed top, with the canvas stripes radiating from the apex. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/2/1.

Hints

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

Hint 1

The height of the cone is the total height minus the height of the cylinder, and the radius is half the diameter.

Hint 2

Slant height uses Pythagoras: $l^{2} = h^{2} + r^{2}$ . The floor is a circle.

Hint 3

Cloth covers only the curved surfaces (no floor). The air fills the whole cylinder plus the whole cone.

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.

(i) Radius $r = \frac{28}{2} = 14$ m. Height of the conical part $h = 18.5 - 8 = 10.5$ m.
½ mark
Slant height $l = h^{2} + r^{2} = (10.5)^{2} + 1 4^{2} = 110.25 + 196 = 306.25 = 17.5$ m.
½ mark
(ii) Floor area $= π r^{2} = \frac{22}{7} \times 14 \times 14 = 616 m^{2}$ .
1 mark
(iii)(a) Cloth used = CSA of cylinder + CSA of cone $= 2 π r H + π r l = 2 \times \frac{22}{7} \times 14 \times 8 + \frac{22}{7} \times 14 \times 17.5$
1 mark
$= 704 + 770 = 1474 m^{2}$
1 mark
(iii)(b) Volume of air = volume of cylinder + volume of cone $= π r^{2} H + \frac{1}{3} π r^{2} h = \frac{22}{7} \times 14 \times 14 \times 8 + \frac{1}{3} \times \frac{22}{7} \times 14 \times 14 \times 10.5$
1 mark
$= 4928 + 2156 = 7084 m^{3}$
1 mark

Answer: (i) 17.5 m; (ii) 616 m²; (iii)(a) 1474 m²; (iii)(b) 7084 m³

Where the marks are

(i) Finds the height of the cone as 10.5 m and the radius as 14 m (½ mark)
(i) Gets slant height 17.5 m using $l = h^{2} + r^{2}$ (½ mark)
(ii) Gets floor area $π r^{2} = 616$ m² (1 mark)
(iii)(a) Writes cloth area = CSA of cylinder + CSA of cone, with correct substitution (1 mark)
(iii)(a) Gets 1474 m² (1 mark)
(iii)(b) Writes volume = cylinder + cone, with correct substitution (1 mark)
(iii)(b) Gets 7084 m³ (1 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 30/2/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 37

Hints

Step-by-step solution

Revise the chapter

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