Chapter 11.7, Problem 12CE

(a)

To determine

To Find: Area all circles similar?

Answer to Problem 12CE

Yes

Explanation of Solution

Given: All circles are similar.

Yes.

All circles are similar because their area and perimeter are dependent on radius.

(b)

To determine

To Find: Ratio of circumference and areas.

Answer to Problem 12CE

Ratio of circumference: $3:4$

Ratio of area: $9:16$

Explanation of Solution

Given: Two circles having radius $9and12$ .

Radius: $9and12$

Circumference

  $\begin{array}{l}{C}_1=2\pi r=2\pi (9)=18\pi \\ C_2=2\pi r=2\pi (12)=24\pi \\ ratio\\ \frac{C_1}{C_2}=\frac{18}{24}=\frac{3}{4}\end{array}$

Scalar factor= $3:4$

Thus

Area

  $3^2:4^2=9:16$