Question

For a circle of radius r and \(\theta\) as central angle, which of the following statements is/are correct?
(A) Volume = 2/3 \(\pi\) r²
(B) Circumference = 2\(\pi\)r
(C) Area = \(\pi\) r²
(D) Area of sector = \(\frac{\pi r^2 \theta}{360}\)
Choose the correct answer from the options given below:

• A. (A), (B) and (D) only
• B. (B), (C) and (D) only
• C. (A), (B), (C) and (D)
• D. (A), (C) and (D) only

Hint:

A circle is a flat shape, so it has no volume. Check the other three against the standard circle and sector formulae.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We must check four statements about a circle of radius \(r\) and a sector with central angle \(\theta\) in degrees. Then we pick the option that lists only the true ones.

Step 2: Key Formulae:
Circumference of a circle: \(2\pi r\).
Area of a circle: \(\pi r^2\).
Area of a sector with central angle \(\theta\) in degrees: \(\frac{\theta}{360} \times \pi r^2\).

Step 3: Check statement (A):
A circle is a flat figure, so it has an area but no volume. Also, \(\frac{2}{3}\pi r^2\) is not the area formula. So (A) is FALSE.

Step 4: Check statement (B):
The distance around a circle is \(2\pi r\). So (B) is TRUE.

Step 5: Check statement (C):
The area of a circle is \(\pi r^2\). So (C) is TRUE.

Step 6: Check statement (D):
A sector is the fraction \(\frac{\theta}{360}\) of the whole circle. So its area is \(\frac{\pi r^2 \theta}{360}\). So (D) is TRUE.

Step 7: Pick the option:
The true statements are (B), (C) and (D). Options (1), (3) and (4) all include (A), which is false. Only option (2) lists (B), (C) and (D).

Final Answer:
Statements (B), (C) and (D) are correct. This is option (2). \[ \boxed{\text{(B), (C) and (D) only}} \]