calculus

The radius of a circle is increasing at a nonzero rate, and at a certain instant, the rate of increase in the area of the circle is numerically equal to the increase in its circumstance. At this instant, the radius of the cirle is...

Here is what I did: (unsure)
pi(r^2)=2pi(r)
r^2-r=0
r(r-2)=0
r=2

  1. 👍
  2. 👎
  3. 👁
  1. no, it is the rates of increase that are equal, so you have to set the derivatives equal.

    dA/dr = 2pi(r)
    dC/dr = 2pi

    so 2pi(r) = 2 pi
    r = 1

    1. 👍
    2. 👎
  2. u forgot that da/dr is twice the rate of dc/dr. so u would make have to multiply dc/dr by 2. this gives u r = 2.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus help thanks!

    The gas law for an ideal gas at absolute temperature T (in kelvins), pressure P (in atmospheres), and volume V (in liters) is PV = nRT, where n is the number of moles of the gas and R = 0.0821 is the gas constant. Suppose that, at

  2. Calculus

    The radius of a circle is increasing. At a certain instant, the rate of increase in the area of the circle is numerically equal to twice the rate of increase in its circumference. What is the radius of the circle at that instant?

  3. Calculus

    a spherical balloon is inflated with gas at the rate of 500 cubic centimeters per minute. how fast is the radius of the balloon increasing at the instant the radius is 30 centimeters?

  4. survey of calculus

    The 4- inch radius of a circle is increasing at a rate of 2 inches per second. How fast is the area increasing?

  1. calculus

    Sand is poured at the rate of 10 m cube /min so as to form a conical pile whose altitude is always equal to the radius of its base a) How fast is the radius increasing when it is 5 meters? b) Find the rate at which the area of its

  2. Calculus

    A spherical balloon is inflated at a rate of 10 cubic feet per minute. How fast is the radius of the balloon changing at the instant the radius is 4 feet? And The radius of a circle is decreasing at a rate of 2 ft/minute. Find the

  3. calculus

    3. The radius r of a sphere is increasing at a constant rate of 0.04 centimeters per second. (Note: The volume of a sphere with radius r is v=4/3pir^3 ). a. At the time when the radius of the sphere is 10 cm, what is the rate of

  4. math

    The radius r of a sphere is increasing at the uniform rate of 0.3 inches per second. At the instant when the surface area S becomes 100pi square inches, what is the rate of increase, in cubic inches per second, in the volume V?

  1. calculas

    4.A paper cup, which is in the shape of a right circular cone, is 16 cm deep and has a radius of 4 cm. Water is poured into the cup at a constant rate of . 3 2cm / sec (a) At the instant the depth is 5 cm, what is the rate of

  2. maths help calculus

    the area of a circle increasing at the rate of 3cm/sec.find the rate of change of the circumference when the radius is 2cm help plz

  3. 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? A. 1/5 B. pi/5 C. 2 D. 2pi E. 25pi

  4. calc 3

    The length script l, width w, and height h of a box change with time. At a certain instant the dimensions are script l = 7 m and w = h = 5 m, and script l and w are increasing at a rate of 6 m/s while h is decreasing at a rate of

You can view more similar questions or ask a new question.