A circle with a radius of r units is dilated by a scale factor of 7 to create a new circle. Which statement about the area of the new circle is true?

A. The area of the new circle is 7 times the area of the original circle.

B. The area of the new circle is 14 times the area of the original circle.

C. The area of the new circle is 49 times the area of the original circle.

D. The area of the new circle is squared root 7 times the area of the original circle.

Answer:

A

Step-by-step explanation:

The scale factor can be defined as the ratio of new dimension of an object after scaling to the original  dimension. The are of the new circle is 49 times the area of the original circle. The correct answer is option C.

Scaling factor is a conversion factor used to change the size of a figure without changing its shape. When the size of a figure is increased, it called scaled up and when it decreases it is called as scaled down.

Given that, Scale factor of circle = 7.

Since, the scale factor of a circle is the ratio of new radius to original radius.

The new radius of circle can be written as,

r' = 7r

Thus, the area of new circle is π × (r')^2= π × (49r^2).

Hence, the area of new circle is 49 times the original circle.

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