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

Step 1: Write the area formula.
The area of a circle depends on the square of its radius.
\[ A = \pi r^2 \]

Step 2: Double the radius.
Replace $r$ with $2r$.
\[ A' = \pi (2r)^2 = 4\pi r^2 \]

Step 3: Compare the two.
The new area is four times the old one, since the radius is squared.
\[ \boxed{\text{Four times}} \]