Question

If the radius of a circle is doubled, its area becomes: 

• A. Four times
• B. Double
• C. Eight times
• D. Remains same Correct Answer: (A) Four times Solution:

Hint:

Whenever a quantity depends on the square of a variable: \[ (x \rightarrow 2x) \] implies \[ x^2 \rightarrow 4x^2 \] Since area of a circle depends on \(r^2\), doubling the radius quadruples the area.

Answer 1

The Correct Option is A

Concept: The area of a circle is directly proportional to the square of its radius. The formula for the area of a circle is \[ A = \pi r^2 \] where \(r\) is the radius.

Step 1: Write the original area. If the original radius is \(r\), then \[ A = \pi r^2 \]

Step 2: Double the radius. The new radius is \[ r' = 2r \] The new area becomes \[ A' = \pi (2r)^2 \] \[ A' = \pi (4r^2) \] \[ A' = 4\pi r^2 \]

Step 3: Compare the two areas. Since \[ A = \pi r^2 \] and \[ A' = 4\pi r^2 \] therefore \[ A' = 4A \] Thus, the new area is four times the original area. \[ \boxed{\text{Area becomes four times}} \] Hence, the correct option is \(\boxed{(A)}\).