If a sector of a circle has an area of 40π sq. units and a central angle of 72°, the radius of the circle is : (A) 200 units (B) 100 units (C) 20 units (D) 10√(2) units

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2025: question 15

Set in the CBSE Class 10 board exam of 2025, paper 30/1/1, section A, question 15, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q15 · 1 mark · MCQAreas Related to Circles

If a sector of a circle has an area of $40 π$ sq. units and a central angle of $7 2^{\circ}$ , the radius of the circle is :

(A)200 units
(B)100 units
(C)20 units
(D) $102$ units

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/1/1.

Hints

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

Hint 1

Use the sector area formula $\frac{θ}{360} π r^{2}$ .

Hint 2

Note that $\frac{72}{360} = \frac{1}{5}$ . Solve for $r^{2}$ .

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.

Area of a sector $= \frac{θ}{36 0 ^{\circ}} \times π r^{2}$ .
$\frac{72}{360} \times π r^{2} = 40 π \Rightarrow \frac{r ^{2}}{5} = 40 \Rightarrow r^{2} = 200$ .
$r = 200 = 102$ units, so the answer is option (D).
1 mark

Answer: $102$ units, option (D)

Where the marks are

Chooses option (D) $102$ units (1 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 paper2025 board paper, set 30/1/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2025: question 15

Hints

Step-by-step solution

Revise the chapter

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