# calculus

posted by .

The diagonal of a square is increasing at a rate of 3 inches per minute. When the area of the square is 18 square inches, how fast(in inches per minute) is the perimeter increasing?

• calculus -

The sides are .707 of the diagonal, and area is s squared, so
Area= .5 diagonal^2

or diagonal= sqrt (2*area)

Perimeter= 4s=4(.707)diagonal

dP/dt= 4*.707 * diagonal/dt
= 4*.707 3in/min

I don't see it vary with the size of the square. check my thinking.

• calculus -

bobpursely is right, the area of 18 in^2 has nothing to do with it.

Here is how I did it

D^2 = 2s^2
D = √2 s
dD/dt = √2 ds/dt
3 = √2 ds/dt ------> ds/dt = 3/√2

P = 4s
dP/dt = 4ds/dt=4(3/√2) = 12/√2 in/min

which is the same as bobpursley's answer

## Similar Questions

1. ### calculus

a spherical snowball with diameter 4 inches is removed from the freezer in June and begins melthing uniformly such that it is shrinking 2 cubic inches per minute. How fast ( in square inches per minute) is the surface area decreasing …
2. ### calculus

The side of a square are increasing at 2 inches per second. How fast is the diagonal increasing when the side is 3 inches?
3. ### calculus

at a certain instant the base of a triangle is 5 inches and is increasing at the rate of 1 inch per minute. At the same instant, the height is 10 inches and is decreasing at the rate of 2.5 inches per minute. Is the area of the triangle …
4. ### Calculus

At a certain instant, each edge of a cube is 5 inches long and the volume is increasing at the rate of 2 cubic inches per minute. How fast is the surface area of the cube increasing?
5. ### Per Calculus

An apple pie has a 12 inch diameter and the angle of one slice is 60 degrees. What is the area of that slice of pie?
6. ### Calculus

A rectangle is 2 feet by 15 inches. Its length is decreasing by 3 inches/minute and its width is increasing at 4 inches/minute. How fast is the a) perimeter changing b) area changing
7. ### AP CALC. AB

Please help me with this problem and please walk me through each step i am really confused. Sand is falling from a rectangular box container whose base measures 40 inches by 20 inches at a constant rate of 300 cubic inches per minute. …
8. ### AB Calculus

I figured out that part "A" is -3/8, but i can't figure out part 2, a or b. please explain and help. thanks. Sand is falling from a rectangular box container whose base measures 40 inches by 20 inches at a constant rate of 300 cubic …
9. ### Calculus

The circumference of a circle is increasing at a rate of 2pi/5 inches per minute. When the radius is 5 inches, how fast is the area of the circle increasing in square inches per minute?
10. ### calculus

Water leaking onto a floor creates a circular pool with an area that increases at the rate of 3 square inches per minute. How fast is the radius of the pool increasing when the radius is 10 inches?

More Similar Questions