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.

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).