Question

The volume of a right circular cone is latex: v=\frac{1}{3}\pi r^2h v = 1 3 π r 2 h . suppose a cone has a constant height of h = 3 cm but its radius is changing. use the differential to estimate the change in volume as the radius changes from 5 cm to 4.64 cm.

Answer 1

V  =  (1/3)·π·r²·h                     First, multiply both sides by 3:

3V  =  π·r²·h                            Now, divide by π·h 

3V / (π·h)  =  r²                       Finally, take the square root of both sides:

±√[ 3V / (π·h) ]  =  r²              If you are in algebra, you need the ±; if you are in geometry, you probably                                                      don't (usaully, you don't have negative radii).