A circle is inside a square. The radius of a circle is increasing at a rate of 4 meters per day and the sides of the square are increasing at a rate of 3 meters per day.

Question

A circle is inside a square.

The radius of a circle is increasing at a rate of

4 meters per day and the sides of the square

are increasing at a rate of 3 meters per day.

When the radius is 3 meters,

and the sides are 17 meters

then how fast is the AREA between the circle and

the square changing?

The rate of change of the AREA enclosed between

the circle and the square is _______ square meters per day.

(Enter your answer as a decimal number rounded to 2 places.)

Answer 1

circle area =pir^2 =9pi

square area = s^2 =17^2>9pi

difference =d = area between them

d = s^2 - pir^2

d' =2ss' - 2pirr'

= 2(17)(3) - 2pi(3)(4)

= 102- 24pi

=about 102-24(3.141593)

=26.60 m^2/day

if you use a less accurate pi=3.14

then you'll get d'=26.64

Answer 2

The rate of change of the area enclosed between the circle and the square is approximately -26.64 square meters per day. The negative sign indicates that the area is decreasing.

Hope so it will help you