For a circle of radius r and as central angle, which of the following statements is/are correct? (A) Volume = 2/3 r^2 (B) Circumference = 2 r (C) Area = r^2 (D) Area of sector = ( r^2 )/360 Choose the correct answer from the options given below: Option 1: (A), (B) and (D) only Option 2: (B), (C) and (D) only Option 3: (A), (B), (C) and (D) Option 4: (A), (C) and (D) only

Answer: (B), (C) and (D) only. Solution: A circle is a plane figure, so it has no volume, making (A) incorrect. Circumference = 2 r and area = r^2 are standard, so (B) and (C) hold. A sector of angle is the fraction /360 of the full circle, giving area r^2/360, so (D) holds. Hence (B), (C) and (D).

Geometry

Circles

Easy

For a circle of radius r and $\theta$ as central angle, which of the following statements is/are correct?

(A) Volume = $\frac{2}{3}\pi r^2$

(B) Circumference = $2\pi r$

(C) Area = $\pi r^2$

(D) Area of sector = $\frac{\pi r^2 \theta}{360}$

Choose the correct answer from the options given below:

(A), (B) and (D) only

(B), (C) and (D) only

(A), (B), (C) and (D)

(A), (C) and (D) only

✅ Correct Option: 2

A circle is a plane figure, so it has no volume, making (A) incorrect. Circumference $= 2\pi r$ and area $= \pi r^2$ are standard, so (B) and (C) hold. A sector of angle $\theta$ is the fraction $\theta/360$ of the full circle, giving area $\pi r^2\theta/360$ , so (D) holds. Hence (B), (C) and (D).

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