Answer :
Answer:
Step-by-step explanation:
a. the area of the pupil can be represented as: Area = π(6 - x)^2 square millimeters.
b. the area of the pupil is 4 times greater after entering the dark room than before entering.
So, the radius of the small circle is 6 - x millimeters.
The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
Therefore, the area of the pupil can be represented as:
Area = π(6 - x)^2 square millimeters.
c. The width of the iris decreases from 4 millimeters to 2 millimeters when entering a dark room. To find how many times greater the area of the pupil is after entering the room compared to before entering, we need to calculate the area in both cases.
Before entering the dark room:
The width of the iris is 4 millimeters, so the radius of the small circle representing the pupil is 6 - 4 = 2 millimeters.
The area of the pupil before entering the dark room can be calculated using the formula:
Area1 = π(2)^2 square millimeters.
After entering the dark room:
The width of the iris is now 2 millimeters, so the radius of the small circle representing the pupil is 6 - 2 = 4 millimeters.
The area of the pupil after entering the dark room can be calculated using the formula:
Area2 = π(4)^2 square millimeters.
To find how many times greater the area of the pupil is after entering the room than before entering, we can divide the area after entering by the area before entering:
Area2 / Area1.
Substituting the values, we have:
π(4)^2 / π(2)^2 = 16 / 4 = 4.
Therefore, the area of the pupil is 4 times greater after entering the dark room than before entering.
Remember, the area of the pupil increases as the iris constricts in response to less light entering the eye.
