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 of the balloon is changing with respect to its surface area when the surface area measures 50 cm^2.

  1. 👍 2
  2. 👎 0
  3. 👁 606
  1. using the area, r = √(s/4π)
    so, v = 4/3 π (s/4π)^(3/2) = 1/(6√π) s^(3/2)
    dv/ds =1/(4√π) s^(1/2) = 1/4 √(s/π)
    at s=50, that would be 5/4 √(2/π)

    1. 👍 0
    2. 👎 3
    👨‍🏫
    oobleck

Respond to this Question

First Name

Your Response

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? V= 4/3*pi*r^3 S= 4 pi r^2

  2. Physics

    Hot air balloons float in the air because of the difference in density between cold and hot air. In this problem, you will estimate the minimum temperature the gas inside the balloon needs to be, for it to take off. To do this,

  3. Physics

    Four objects - a hoop, a solid cylinder, a solid sphere, and a thin, spherical shell - each has a mass of 4.59 kg and a radius of 0.252 m. (a) Find the moment of inertia for each object as it rotates about the axes shown in the

  4. 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

  1. Physics

    two identical metallic ball spherical shells A and B charges 4Q and -10c are kept a certain distance apart a third uncharged sphere C is first placed in contact with sphere A and then with sphere B the sphere B are bought in

  2. PHYSICS! HELIUM BALLON

    Under standard conditions, the density of air is 1.293 kg/m3 and that of helium is 0.178 kg/m3. A spherical helium balloon lifts a basket plus cargo of mass 277.0 kg. What must be the minimum diameter of the spherical balloon?

  3. math-calculus

    A spherical party balloon is being inflated with helium pumped in at a rate of 12 cubic feet per minute. How fast is the radius growing at the instant when the radius has reached 1 ft?

  4. Word Problem-Calculus

    A spherical balloon is being inflated in such a way that its radius increases at a rate of 3 cm/min. If the volume of the balloon is 0 at time 0, at what rate is the volume increasing after 5 minutes? my answer is 45 cm/min. is

  1. Calculus Homework

    You are blowing air into a spherical balloon at a rate of 7 cubic inches per second. The goal of this problem is to answer the following question: What is the rate of change of the surface area of the balloon at time t= 1 second,

  2. Physics

    A rigid tank having a volume of 0.100 m3 contains helium gas at 150 atm. How many balloons can be inflated by opening the valve at the top of the tank? Each filled balloon is a sphere 0.300 m in diameter at an absolute pressure of

  3. calculus

    The radius of a spherical balloon is increasing at a rate of 2 centimeters per minute. How fast is the volume changing when the radius is 8 centimeters? Note: The volume of a sphere is given by 4(pi)r^3

  4. 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?

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