Please note that we are dealing with an Ellipsoid and Hemisphere..
The formula for the volume of an ellipsoid is given below;
"Volume of an ellipsoid" rArr V_e = 4/3piabcVolume of an ellipsoid⇒Ve=43πabc
The formula for the volume of a hemisphere is given below;
"Volume of a hemisphere" rArr V_h = 2/3pir^3Volume of a hemisphere⇒Vh=23πr3
Since we are removing a portion of a Hemisphere from an Ellipsoid, it means that we need to subtract the volume of a hemisphere from the ellipsoid which is given below;
"Remaining volume of an ellipsoid" color(white)x R_(ve) = V_e - V_hRemaining volume of an ellipsoidxRve=Ve−Vh
R_(ve) = V_e - V_hRve=Ve−Vh
Where;
R_(ve) = "Remaining volume of an ellipsoid"Rve=Remaining volume of an ellipsoid
V_e = "Volume of an ellipsoid"Ve=Volume of an ellipsoid
V_h = "Volume of a hemisphere"Vh=Volume of a hemisphere
a, b, c = "lengths"a,b,c=lengths
r = "radius"r=radius
R_(ve) = V_e - V_hRve=Ve−Vh
V_e = 4/3piabcVe=43πabc
V_h = 2/3pir^3Vh=23πr3
a, b, c = 5, 5, 8 "respectively"a,b,c=5,5,8respectively
r = 3r=3
pi = 3.142π=3.142
Hence substituting the values into the formula;
R_(ve) = V_e - V_hRve=Ve−Vh
R_(ve) = 4/3pi(5 xx 5 xx 8)- 2/3pi(3)^3Rve=43π(5×5×8)−23π(3)3
R_(ve) = 4/3pi(200)- 2/3pi(27)Rve=43π(200)−23π(27)
R_(ve) = (4(200))/3 pi - (2(27))/3 piRve=4(200)3π−2(27)3π
R_(ve) = 800/3 pi - 54/3 piRve=8003π−543π
R_(ve) = (800 - 54)/3 piRve=800−543π
R_(ve) = 746/3 piRve=7463π
R_(ve) = 248.67 piRve=248.67π
R_(ve) = 248.67 xx 3.142Rve=248.67×3.142
R_(ve) = 781.31cm^3Rve=781.31cm3
Therefore the remaining volume of the ellipsoid is 781.31cm^3781.31cm3