The area of a circle with radius is given by the power function . What happens to the area of the circle when the radius is multiplied by 3?
A) The area increases by a factor of 9.
B) The area is also multiplied by 3.
C) The area increases by .
D) Not enough information.
E) The area increases by .

Question

The area of a circle with radius  is given by the power function  . What happens to the area of the circle when the radius is multiplied by 3?
A) The area increases by a factor of 9. 
B) The area is also multiplied by 3. 
C) The area increases by . 
D) Not enough information. 
E) The area increases by .

Quizplus · Accepted Answer

The area of a circle is proportional to the square of its radius. When the radius is multiplied by 3, the new radius becomes 33 times the original radius. Therefore, the new area is 11 times 33 squared times the original area, which simplifies to 9 times the original area. Therefore, the area increases by a factor of 9.

The Area of a Circle with Radius Is Given