MathsCBSE Class 10 · Basic · Sample paper, session 2023-24 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic sample paper 2023-24: question 25(a)

From the official CBSE sample question paper for 2023-24, section B, question 25(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25(a) · 2 marks · Very short answerAreas Related to Circles

Find the diameter of a circle whose area is equal to the sum of the areas of two circles of radii 40 cm and 9 cm.

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

Write the area of each circle as $π r^{2}$ and set up the equation.

Hint 2

$π$ cancels from both sides. Find $R$ , then remember that the question asks for the diameter.

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.

Let R be the radius of the required circle. Then $π R^{2} = π (40)^{2} + π (9)^{2}$
½ mark
$R^{2} = 4 0^{2} + 9^{2} = 1600 + 81 = 1681$
½ mark
$R = 41$ cm
½ mark
Diameter $= 2 R = 2 \times 41 = 82$ cm
½ mark

Answer: Diameter = 82 cm

Where the marks are

Forms the equation $π R^{2} = π (40)^{2} + π (9)^{2}$ (1/2 mark)
Gets $R^{2} = 1681$ (1/2 mark)
$R = 41$ cm (1/2 mark)
Diameter = 82 cm (1/2 mark)

Revise the chapter

Chapter: Areas Related to Circles (notes, formulas, where marks are lost and every past question)
Topic: Area of a Sector of a Circle

Practise this chapterBoard-style questions from Areas Related to Circles, 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.

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CBSE Class 10 Mathematics Basic sample paper 2023-24: question 25(a)

Hints

Step-by-step solution

Revise the chapter

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