math

The area of a spherical balloon expand at a rate of 0.4cm square/s .find the rate at which its volume expand when the radius is 12cm

  1. 👍 0
  2. 👎 0
  3. 👁 217
  1. a = 4πr^2
    da/dt = 8πr dr/dt

    v = 4/3 πr^3 = ar/3
    dv/dt = 1/3 (r da/dt + a dr/dt)
    Now just plug in your numbers

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Mathematics

    A spherical balloon is being inflated. Given that the volume of a sphere in terms of its radius is v(r)=(4/3)(pi(r^3)) and the surface area of a sphere in terms of its radius is s(r)=4pi(r^2), estimate the rate at which the volume

  2. Math

    A spherical balloon is being inflated. Given that the volume of a sphere in terms of its radius is V(r) =4/3 πr^3 and the surface area of a sphere in terms of its radius is S(r) = 4 πr^2, estimate the rate at which the volume of

  3. physics

    Hot air balloon A is rising upward a rate of 5.0 m/s. A passenger aboard balloon A observes balloon B rising upward at a relative rate of 7.5 m/s. What is the velocity of balloon B relative to the ground? Assume that up is

  4. Math Advanced Functions

    A spherical balloon is being inflated. Given that the volume of a sphere in terms of its radius is V(r)= 4/3 πr^3 and the surface area of a sphere in terms of its radius is S(r)= 4πr^2, estimate the rate at which the volume of

  1. Physics

    I need help on two problems :P 1. A spherical balloon is partially blown up and its surface area is measured. More air is added increasing the volume of the balloon. If the surface area of the balloon expands by a factor of 2.0

  2. Math(Please help)

    Related Rates: Gas is escaping from a spherical balloon at the rate of 2ft^3/min. How fast is the surface area shrinking (ds/dt) when the radius is 12ft? (A sphere of radius r has volume v=4/3 pi r^3 and surface area S=4pi r^2.)

  3. 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

  4. calculus

    Melting Snowball: A spherical snowball melts at a rate proportional to its surface area. Show that the rate of change of the radius is constant. (Hint: Surface Area =4(pi)r^2)

  1. Math

    A spherical balloon is to be deflated so that its radius decreases at a constant rate of 12 cm/min. At what rate must air be removed when the radius is 5 cm? Must be accurate to the 5th decimal place. It seems like an easy

  2. math

    The volume V of a sphere of radius r is given by the formula V (r) = (4/3)πr^3. A balloon in the shape of a sphere is being inflated with gas. Assume that the radius of the balloon is increasing at the constant rate of 2 inches

  3. Physics

    Hot air balloon A is rising upward at a rate of 10.0 m/s. A passenger aboard balloon A observes balloon B going down at a relative rate of 12.5 m/s. What is the velocity of balloon B relative to the ground? Assume that up is

  4. calculus : related rates

    a balloon rises at a rate of 3 meters per second from a point on the ground 30 meters from an observer. find the rate of change of the angle of elevation of the balloon from the observer when the balloon is 30 meters above the

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