For a circle of radius r and \(\theta\) as central angle, which of the following statements is/are correct?
(A) Volume = 2/3πr2
(B) Circumference = 2πr
(C) Area = πr2
(D) Area of sector = \(\displaystyle\frac{\pi r^{2}\theta}{360}\)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (B), (C) and (D) only
A circle is a flat (two-dimensional) figure: it has a length round it (circumference) and an area, but no volume.
(A) Volume = 2/3πr2 Incorrect. A circle has no volume. The nearest formula, \(\frac{2}{3}\pi r^{3}\), is the volume of a hemisphere, a solid.
(B) Circumference = 2πr Correct. The circumference is \(\pi\) times the diameter, and the diameter is \(2r\).
(C) Area = πr2 Correct. This is the standard area of a circle of radius \(r\).
(D) Area of sector = \(\frac{\pi r^{2}\theta}{360}\) Correct. A central angle of \(\theta\) degrees is \(\frac{\theta}{360}\) of a full turn, so the sector is that fraction of the circle’s area: \(\frac{\theta}{360}\times\pi r^{2}\).