An ellipsoid has radii with lengths of 8 , 8 , and 12 . A portion the size of a hemisphere with a radius of 6 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

1 Answer
Jul 20, 2018

color(purple)("Remaining volume of ellipsoid " V_r ~~ 2764.6 " cubic umits"

Explanation:

http://www.web-formulas.com/Math_Formulas/Geometry_Volume_of_Ellipsoid.aspx

"Vol. of ellipsoid " = V_e = (4/3) pi a * b * c

"If a = b = c, it becomes a sphere and vol. " = V_s = (4/3) pi r^3

"Vol. of hemisphere = V_h = V_s / 2 = (2/3) pi r^3

"Given : " a = 8, b = 8, c = 12, r = 6

"Remaining vol " V_r = V_e - V_h = (4/3) pi a^2 c - (2/3) pi r^3, a = b

V_r = (4/3) * pi * 8^2 * 12 - (2/3) * pi * 6^3

color(purple)("Volume of remaining ellipsoid " V_r ~~ 2764.6 " cubic umits"