Chapter 11.5, Problem 22WE

To determine

To determine the circumferences and areas of the circles of light on the screen and on the wall.

Answer to Problem 22WE

Area of the circle on the screen is $\pi {\left(2\right)}^2=4\pi$ ft².

Circumference of circle on the screen is $2\pi \left(2\right)=4\pi$ ft.

Area of the circle on the wall is $\pi {\left(4\right)}^2=16\pi$ ft².

Circumference of circle on the wall is $2\pi \left(4\right)=8\pi .$ ft.

Explanation of Solution

Given information :

Radius of circle is 2 ft. on the screen that is 10 ft. from projector.

Area of the circle on the screen is $\pi {\left(2\right)}^2=4\pi$ ft².

Circumference of circle on the screen is $2\pi \left(2\right)=4\pi$ ft.

Now the circle on wall will have radius 4ft. using the concept of similarity as shown.

  

Area of the circle on the wall is $\pi {\left(4\right)}^2=16\pi$ ft².

Circumference of circle on the wall is $2\pi \left(4\right)=8\pi .$ ft.