Pre-Calculus

The surface ares S (in square meters) of a hot air ballon is given by s(r)=4 pi r^2 where r is radius of balloon (in meters). If the radius r is increasing with time (in seconds) according to the formula r(t) = 2/3t^3, t is greater than or equal to 0, find the surface area S of the balloon as a function of the time t.


Ok, your first function give S(r) or surface area as a function of the radius. You second function r(t)=(2/3)t^3 gives the radius as a function of time. If you compose the function to get
S(r(t)) = 4*pi*((2/3)t^3)^2
you have the surface area as a function of time alone. You can write it as
S(t) = something you can simplify.

  1. 👍
  2. 👎
  3. 👁

Respond to this Question

First Name

Your Response

Similar Questions

  1. science

    when that air under the envelope is heated , the balloon lifts . which of the following statement is true A. hot air balloons use radiation to rise B. hot air balloons use conduction to rise C. hot air balloons use convection to

  2. chemistry

    The figure shows a cube of air at pressure 1.0 atm above a hot surface on Earth. Contact with the hot surface causes the volume of the air to expand from 2.00 × 105 L to 2.20 × 105 L by the transfer of 8.2 × 106 J of heat.

  3. Physics

    A hot-air balloon is accelerating upward under the influence of two forces, its weight and the buoyant force. For simplicity, consider the weight to be only that of the hot air within the balloon, thus ignoring the balloon fabric

  4. Science Halp

    1 When the air under the envelope is heated, the balloon lifts. Which of the following statements is true. a. Hot air balloons use radiation to rise b. Hot air balloons use conduction to rise c. Hot air balloons use convection to

  1. 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,

  2. Physics

    A weather ballon is designed to expand to a maximum radius of 20 m at its working altitude, where the air pressure is 0.030 atm and the temperature is 200 K. If the ballon is filled at atmospheric pressure and 300 K, what is its

  3. calculus problem I have tried 100 times

    A tank in the shape of an inverted right circular cone has height 5 meters and radius 4 meters. It is filled with 2 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the

  4. Spherical Trigonometry

    *Approximate the angle of elevation of the sun if a box 5 meters tall casts a shadow 4 meters long on level ground. *As a weather ballon rises vertically its angle of elevation from a point P on the level ground 110km.from the

  1. Algebra

    Two hot air ballons are in flight above a field. The first balloon is 30 meters above ground and rising 25 meters per minute. The second ballon is 300 meters above ground and descending 20 meters per minute. When will the two

  2. Chemistry

    The total mass that can be lifted by a balloon is given by the difference between the mass of air displaced by the balloon and the mass of the gas inside the balloon. Consider a hot air balloon that approximates a sphere 5.00 m in

  3. Geometry

    . The Great Pyramid of Cheops has a square base of 230 meters on each side, and a height of 147 meters. Find the exposed surface area in square meters

  4. Physics

    A jetliner flies west 2,000 miles from Chicago you San Francisco. It has an average speed of 635 mph relative to the air. What is the velocity of the jetliner relative to the earth of the wind is blowing at 160 mph from the west

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