Post a New Question

calculus

posted by .

A spherical balloon is being inflated at a rate of 10 cubic inches per second. How fast is the radius of the balloon increasing when the surface area of the balloon is square inches? Enter your answer correct to 3 decimal places.

  • calculus -

    well, you forgot to say what that area was but anyway
    for a sphere
    V = (4/3) pi r^3
    A = dV/dr = pi r^2

    dV/dt = dV/dr * dr/dt = pi r^2 dr/dt

    dV/dt = 10 given
    so
    10 = pi r^2 dr/dt

    put in the r from the surface area you forgot to type and solve for dr/t

  • calculus -

    OOps How fast is the radius of the balloon increasing when the surface area of the balloon is 2pi square inches?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    Air is being pumped into a spherical balloon so that its volume increases at a rate of 30 cubic centimeters per second. How fast is the surface area of the balloon increasing when its radius is 19 cm?
  2. 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?
  3. calculus

    Air is being pumped into a spherical balloon so that its volume increases at a rate of 80 cubic centimeters per second. How fast is the surface area of the balloon increasing when its radius is 8 cm?
  4. Calculus

    A spherical balloon is being inflated at a rate of 10 cubic inches per second. How fast is the radius of the balloon increasing when the surface area of the balloon is 2pi square inches?
  5. AP calculus AB

    A spherical balloon is being filled with air in such a way that its radius is increasing at a rate of 2 centimeters per second. At what rate is the volume of the balloon changing at the instant when its surface has an area of 4 pi …
  6. Calculus

    Air is being pumped into a spherical balloon so that its volume increases at a rate of 80 cm^3 per second. How fast is the surface area of the balloon increasing when its radius is 9cm?
  7. Math

    A spherical balloon with a surface area of 36pi square inches is inflated further until its diameter has increased by 50%. The surface area of the balloon is now?
  8. Calculus

    A spherical water balloon is being filled with water at the rate of 125 cubic inches per minute. At what rate is the radius increasing when the radius is 10 inches?
  9. Calculus

    A spherical balloon is being inflated and the radius of the balloon is increasing at a rate of 2cm/min. At what rates are the volume and surface area of the balloon increasing when the radius is 5cm?
  10. Calculus

    A spherical balloon is inflated with gas at the rate of 20 cubic feet per minute. How fast is the radius of the balloon increasing at the instant the radius is (a) 1 foot and (b) 2 feet?

More Similar Questions

Post a New Question