MathsCBSE Class 10 · Basic · Board exam 2023, set 430/6/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2023: question 34

Set in the CBSE Class 10 board exam of 2023, paper 430/6/1, section D, question 34, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q34 · 5 marks · Long answerCompetency-basedSurface Areas and Volumes

An ice-cream filled cone having radius 5 cm and height 10 cm is as shown in the figure. Find the volume of the ice-cream in 7 such cones.

Figure in the paper: An ice-cream cone shape: a hemisphere on top (flat face at the top with centre marked) with radius 5 cm, and a cone below it pointing downward. The radius is marked as 5 cm from the centre to the right edge, and the vertical height from the rim to the tip is marked as 10 cm. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/6/1.

Hints

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

Hint 1

The ice-cream is a cone with a hemisphere on top; both have radius 5 cm.

Hint 2

The 10 cm includes the hemisphere's radius, so the cone's height is 10 − 5; add the two volumes and multiply by 7.

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.

The 10 cm is the total height of the ice-cream (hemisphere top to cone tip), and the hemisphere has radius $r = 5$ cm, so height of conical part $h = 10 - 5 = 5$ cm.
½ mark
Volume of ice-cream in one cone = volume of cone + volume of hemisphere $= \frac{1}{3} π r^{2} h + \frac{2}{3} π r^{3} = \frac{1}{3} π r^{2} (h + 2 r)$
1 mark
$= \frac{1}{3} \times \frac{22}{7} \times 5 \times 5 \times (5 + 10)$
1½ marks
$= \frac{22 \times 25 \times 15}{21}$ cm³ $(= \frac{2750}{7} \approx 392.86 cm^{3})$
1 mark
Volume in 7 cones $= 7 \times \frac{22 \times 25 \times 15}{21}$
½ mark
$= \frac{8250}{3} \times \dots$ simplifies to $= \frac{22 \times 25 \times 15}{3} = 2750$ cm³
½ mark

Answer: 2750 cm³

Where the marks are

Height of cone = 10 − 5 = 5 cm (½ mark)
Volume = cone + hemisphere formula (1 mark)
Correct substitution (1½ marks)
Volume of one cone = 22×25×15/21 cm³ (1 mark)
Multiplies by 7 (½ mark)
Total = 2750 cm³ (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 paper2023 board paper, set 430/6/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2023: question 34

Hints

Step-by-step solution

Revise the chapter

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