Posted by Yoona on Tuesday, January 3, 2012 at 12:02am.
3. The radius r of a sphere is increasing at a constant rate of 0.04 centimeters per second. (Note: The volume of a sphere with radius r is v=4/3pir^3 ).
a. At the time when the radius of the sphere is 10 cm, what is the rate of increase of its volume?
b. At the time when the volume of the sphere is 36pi cubic centimeters, what is the rate of increase of the area of a cross section through the center of the sphere?
c. At the time when the volume and the radius of the sphere are increasing at the same numerical rate, what is the radius?

calculus  Reiny, Tuesday, January 3, 2012 at 9:44am
dV/dt = 4πr^2 dr/dt
a) when r=10 and dr/dt = .04
dV/dt = 4π(100)(.04) = ...
b) when V = 36π
36π = (4/3)πr^3
27 = r^3
r = 3
cross section is a circle, A = πr^2
dA/dt = 2πr dr/dt
= 2π(3)(.04)
= ..
c) dV/dt = 4πr^2 dr/dt, but dr/dt = dV/dt = .04
.04 = 4πr^2 (.04)
4πr^2 = 1
r^2 = 1/(4π)
r = 1/(2√π) = ...

application of derivatives  neha, Thursday, September 4, 2014 at 2:18pm
The radius of an air bubble is increasing at what rate is the volume of the bubble increasing when the radius is 1 centimetre?

calculus  ps, Saturday, May 21, 2016 at 5:00am
The volume of sphere is increasing at the rate of 1200c.cm/sec. the rate increase in its surface area when the radius is 10cm is

calculus  Anonymous, Thursday, January 19, 2017 at 11:00pm
So confusing
Answer This Question
Related Questions
 Calculus  4. At time t, t>0, the volume of a sphere is increasing at a rate ...
 calculus  The radius of a spherical balloon is increasing at a rate of 2 ...
 Calculus Can you help me solve for dr/dt  How fast does the radius of a ...
 Calculus  The volume of a cone of radius r and height h is given by V=1/3pir^2h...
 Calculus (Parts A and B done, just help with C)  The radius, r, of a sphere is ...
 PreCalculus  As a balloon in the shape of a sphere is being blown up, the ...
 Math( Can you help me with starting this problem)  How fast does the radius of ...
 college physics  Two solid spheres A and B are made from the same material. The...
 college physics  Two solid spheres A and B are made from the same material. The...
 physics  Two solid spheres A and B are made from the same material. The mass of...
More Related Questions