Question

The circle will be enlarged by a scale factor of 4.

3 in.
What will be the area of the new circle?
O
O
121 square inches
361 square inches
1241 square inches
1441 square inches

Answer 1

Answer: D

Explanation:

Answer 2

The area of the new circle is
`144\pi \ in^2`

Explanation:

Given:

radius of the circle = 3 in.

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared.

Let

z-----> the scale factor

x-----> the area of the enlarged circle

y-----> the area of the original circle

So;

`z^2= (x)/(y)`

In this problem we have

`z=4` ----> the scale factor

The area of the original circle is equal to

`y = \pi r^2= \pi (3)^2= 9\pi \ in^2`

Now substituting value of y and solve for x we get;

`4^2=(x)/(9\pi)\\ \\x= 16*9\pi= 144\pi \ in^2`

Hence Area of the new Circle is
`144\pi \ in^2`

Also The area of the enlarged circle is 16 times the area of the original circle.