MathsCBSE Class 10 · Basic · Sample paper, session 2023-24 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic sample paper 2023-24: question 34(a)

From the official CBSE sample question paper for 2023-24, section D, question 34(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q34(a) · 5 marks · Long answerSurface Areas and Volumes

A medicine capsule is in the shape of a cylinder with two hemispheres stuck at each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.

Figure in the paper: A capsule shape: a cylinder with a hemispherical cap at each end. The overall length is marked 14 mm and the diameter (width) is marked 5 mm. A vertical line marks the junction between the two hemispherical halves. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

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

Hint 2

Surface area = CSA of cylinder + 2 × CSA of hemisphere ( $2 π r^{2}$ each).

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 cylinder and of each hemisphere: $r = \frac{5}{2}$ mm.
Height of the cylinder: $h = 14 - 2 r = 14 - 5 = 9$ mm.
1 mark
CSA of cylinder $= 2 π r h = 2 \times \frac{22}{7} \times \frac{5}{2} \times 9 = \frac{990}{7} mm^{2}$
1 mark
CSA of one hemisphere $= 2 π r^{2} = 2 \times \frac{22}{7} \times (\frac{5}{2})^{2} = \frac{275}{7} mm^{2}$
1 mark
CSA of two hemispheres $= 2 \times \frac{275}{7} = \frac{550}{7} mm^{2}$
1 mark
Surface area of capsule $= \frac{990}{7} + \frac{550}{7} = \frac{1540}{7} = 220 mm^{2}$
1 mark

Answer: Surface area = 220 mm²

Where the marks are

Radius 2.5 mm and cylinder height 9 mm (1 mark)
CSA of cylinder $\frac{990}{7}$ mm² (1 mark)
CSA of one hemisphere $\frac{275}{7}$ mm² (1 mark)
CSA of two hemispheres $\frac{550}{7}$ mm² (1 mark)
Total surface area 220 mm² (1 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 paperSample paper 2023-24 (Basic): 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 Basic sample paper 2023-24: question 34(a)

Hints

Step-by-step solution

Revise the chapter

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