Posted by Eli on Tuesday, October 18, 2011 at 3:01pm.
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)

calculus  Steve, Tuesday, October 18, 2011 at 3:41pm
dV/dt = kA.
V = (4/3) π r^3 and A = 4 π r^2
dV/dt = d/dt((4/3) π r^3) = (4/3) π 3 r^2 (dr/dt)
Now let's plug that into the first equation:
(4/3) π 3 r^2 (dr/dt) = k A = k(4 π r^2) = 4 π k r^2
So when we simplify by dividing left and right sides by 4 π r^2, we get:
dr/dt = k
which is saying exactly what we wanted to prove: that dr/dt is constant.

calculus  amy, Saturday, May 19, 2012 at 8:06pm
Steve you are so smart. thank you. you don't how much it helped me. you save my life from this MMAD MATH INSTRUCTOR
Answer This Question
Related Questions
 calculus  A snowball has a radius of 3 inches. Assume the rate with which the ...
 Calculus  A snowball has a radius of 3 inches. Assume the rate with which the ...
 calculus  A snowball is melting at the rate of 2 inches per hour. How fast is ...
 calculus  A spherical snowball is placed in the sun. The snowball melts so that...
 Calc  A spherical snowball is placed in the sun. The snowball melts so that it'...
 Calculus  A certain calculus student hit Mrs. Evans in the head with a snowball...
 Calc  A spherical snowball is placed in the sun. The snowball melts so that it'...
 Calculus 1  A spherical snowball melts in such a way that its surface area ...
 AP Calc  A spherical snowball is uniformly melting art of rate of pi/18 in^3/...
 calc  The sun is shining and a spherical snowball of volume 210 ft3 is melting ...
More Related Questions