Question

A circle is dilated by a scale factor of 1.5 to create a new circle. The area of the new circle is 1.5 times the area of the original circle.
True or false??

Answer 1

Given:

The given statement is "A circle is dilated by a scale factor of 1.5 to create a new circle. The area of the new circle is 1.5 times the area of the original circle."

To find:

Whether the given statement in true or false.

Solution:

Area of circle is

$A=\pi r^2$

Where, r is the radius of the circle.

Let $r_1$ be the radius of the original circle. So, the area of the circle is

$A_1=\pi (r_1)^2$

The circle is dilated by a scale factor of 1.5 to create a new circle. So, the radius of the new circle is:

$r_2=1.5r_1$

The area of the new circle is

$A_2=\pi (r_2)^2$

$A_2=\pi (1.5r_1)^2$

$A_2=2.25\pi (r_1)^2$

$A_2=2.25A_1$

The area of the new circle is 2.25 times the area of the original circle.

Therefore, the given statement is false.