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

CBSE Class 10 Mathematics Standard 2024: question 38

Set in the CBSE Class 10 board exam of 2024, paper 30/4/1, section E, question 38, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q38 · 4 marks · Case-basedCompetency-basedSurface Areas and Volumes

Tamper-proof tetra-packed milk guarantees both freshness and security. This milk ensures uncompromised quality, preserving the nutritional values within and making it a reliable choice for health-conscious individuals.

500 mL milk is packed in a cuboidal container of dimensions 15 cm $\times$ 8 cm $\times$ 5 cm. These milk packets are then packed in cuboidal cartons of dimensions 30 cm $\times$ 32 cm $\times$ 15 cm.

Based on the above given information, answer the following questions :

(i)
Find the volume of the cuboidal carton.
1 mark
(ii)
(a) Find the total surface area of a milk packet.
2 marks
OR
(ii)
(b) How many milk packets can be filled in a carton ?
2 marks
(iii)
How much milk can the cup (as shown in the figure) hold ?
1 mark

Figure in the paper: Three images: a plain cuboidal carton (unlabelled), a tetra-pack milk packet labelled MILK, and a cylindrical cup. The cup is drawn with its height labelled 7 cm (height of the cup, with a handle on the right side) and its base labelled 5 cm. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/4/1.

Hints

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

Hint 1

The carton and the packet are cuboids; recall the cuboid formulas for volume and total surface area.

Hint 2

For the number of packets, compare the space in the carton with the space one packet takes up.

Hint 3

The cup is a cylinder, so its capacity is $π r^{2} h$ .

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) Volume of carton $= l \times b \times h = 30 \times 32 \times 15$
½ mark
(i) $= 14400 cm^{3}$
½ mark
(ii)(a) TSA of the packet $= 2 (l b + bh + h l) = 2 (15 \times 8 + 8 \times 5 + 5 \times 15) = 2 (120 + 40 + 75)$
1 mark
(ii)(a) $= 470 cm^{2}$
1 mark
(ii)(b) Volume of one packet $= 15 \times 8 \times 5 = 600 cm^{3}$ , so the number of packets $= \frac{30 \times 32 \times 15}{15 \times 8 \times 5} = \frac{14400}{600}$
1 mark
(ii)(b) $= 24$ packets. They fit exactly, as $2 \times 4 \times 3$ along the 30 cm, 32 cm and 15 cm edges.
1 mark
(iii) The cup is a cylinder with radius 5 cm and height 7 cm. Volume $= π r^{2} h = \frac{22}{7} \times 5 \times 5 \times 7$
½ mark
(iii) $= 550 cm^{3} = 550$ mL
½ mark

Answer: (i) 14400 cm³; (ii)(a) 470 cm²; (ii)(b) 24 packets; (iii) 550 cm³ (550 mL)

Where the marks are

(i) Uses $l \times b \times h$ (½ mark) and gets 14400 cm³ (½ mark)
(ii)(a) Uses $2 (l b + bh + h l)$ with correct values (1 mark)
(ii)(a) Gets 470 cm² (1 mark)
(ii)(b) Divides the carton volume by the packet volume (1 mark)
(ii)(b) Gets 24 packets (1 mark)
(iii) Uses $π r^{2} h$ with r = 5, h = 7 (½ mark)
(iii) Gets 550 cm³ or 550 mL (½ 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 paper2024 board paper, set 30/4/1 (Standard): 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 Standard 2024: question 38

Hints

Step-by-step solution

Revise the chapter

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