Chapter 7.3, Problem 36E

To determine

The polynomial representing the area of pupil and change in the area of pupil after entering the room before entering the room.

Answer to Problem 36E

1. The polynomial representing the area of pupil is $\pi r^2$ .
2. After entering the room, the area of pupil is $4$ times greater than before entering the room.

Explanation of Solution

Given information: The width of iris of an eye decreases from $4mm$ to $2mm$ after entering a dark room.

Calculation:

1. Since the pupil of the eye is circular,

  $\therefore$ Area of pupil= $\pi r^2$ ,where ‘ $r$ ’ is the radius of the pupil.

2. From figure, radius of iris and pupil (combined) $=6mm$

   Radius of the pupil before entering the room $=6-4$

     $=2$

   So, the area of the pupil before entering the room $=\pi {(2)}^2$

     $=4\pi$

   Radius of the pupil after entering the room $=4$

   So, the area of the pupil after entering the room $=\pi {(4)}^2$

     $=16\pi$

     $=4(4\pi )$

     $=4$ times the area of the pupil before entering the room