What is the area of a semi-circle of diameter 'd'? (A) 1/16π d² (B) 1/4π d² (C) 1/8π d² (D) 1/2π d²

MathsCBSE Class 10 · Standard · Board exam 2023, set 30/4/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2023: question 5

Set in the CBSE Class 10 board exam of 2023, paper 30/4/1, section A, question 5, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q5 · 1 mark · MCQAreas Related to Circles

What is the area of a semi-circle of diameter 'd'?

(A) $\frac{1}{16} π d^{2}$
(B) $\frac{1}{4} π d^{2}$
(C) $\frac{1}{8} π d^{2}$
(D) $\frac{1}{2} π d^{2}$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/4/1.

Hints

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

Hint 1

A semicircle has half the area of a full circle.

Hint 2

Replace $r$ by $d /2$ in $\frac{1}{2} π r^{2}$ .

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.

The radius is $r = \frac{d}{2}$ .
Area of the semicircle $= \frac{1}{2} π r^{2} = \frac{1}{2} π \cdot \frac{d ^{2}}{4} = \frac{1}{8} π d^{2}$ . So the answer is option (C).
1 mark

Answer: $\frac{1}{8} π d^{2}$ , option (C)

Where the marks are

Chooses option (C) $\frac{1}{8} π d^{2}$ (1 mark)

Revise the chapter

Chapter: Areas Related to Circles (notes, formulas, where marks are lost and every past question)

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 paper2023 board paper, set 30/4/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2023: question 5

Hints

Step-by-step solution

Revise the chapter

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