The image above is an ellipsoid.
To compute the area of an ellipsoid, three essential parameters are needed and this parameters are axis (a), axis (b) and axis (c).
The formula for calculating the area of an ellipsoid:
A = 4π((ab)1.6 + (ac)1.6 + (bc)1.6⁄3)1 / 1.6
Where;
A = Area of the ellipsoid
a = Axis of the ellipsoid
b = Axis of the ellipsoid
c = Axis of the ellipsoid
Let’s solve an example;
Find the the area of an ellipsoid when the axis (a) of the ellipsoid is 12 cm, axis (b) of the ellipsoid is 6 cm and axis (c) of the ellipsoid is 2 cm.
This implies that;
a = Axis of the ellipsoid = 12 cm
b = Axis of the ellipsoid = 6 cm
c = Axis of the ellipsoid = 2 cm
A = 4π((ab)1.6 + (ac)1.6 + (bc)1.6⁄3)1 / 1.6
A = 4π(((12)(6))1.6 + ((12)(2))1.6 + ((6)(2))1.6⁄3)1 / 1.6
A = 4π(((72)1.6 + (24)1.6 + (12)1.6)⁄3)1 / 1.6
A = 4π(((936.98) + (161.56) + (53.29))⁄3)1 / 1.6
A = 4π((1151.84)⁄3)1 / 1.6
A = 4π(383.946)1 / 1.6
A = 4π(383.946)0.625
A = 4π(41.2258)
A = (12.566)(41.2258)
A = 518.059
Therefore, the area of the ellipsoid is 518.059 cm2.