The volume of the horns from bighorn sheep was estimated by researchers using the equation

where h is the length of a horn segment (in centimeters) and r₁ and r₂ are the radii of the two ends of the horn segment (in centimeters).

(a) Determine the volume of a segment of horn that is 40 cm long with radii of 5 cm and 3 cm, respectively.
(b) Use the total differential to estimate the volume of the segment of horn if the horn segment from part (a) was actually 42 cm long with radii of 5.1 cm and 2.9 cm, respectively. Compare this with the actual volume.

Transcribed Image Text:

hπ V = - 3 -(r² + r₁ r₂ + r²),