In the same way that a circle turns into a solid sphere, an ellipse can become a solid "ellipsoid".

There are two special types of ellipsoid.

Suppose if we have a sphere and stretch it to make a longer and thinner shape (a bit like a rugby ball or a melon). In such case it is called a prolate ellipsoid. If we chop it in half to get a circle, then the volume is the area of the circle times 2/3rd of the major axis. (The major axis is the maximum length from the one end to the other.)

However if we have a sphere and squash it to make a shorter fatter shape (a bit like a burger). In such case it is called an oblate ellipsoid. If we chop it through the middle to get a circle, then the volume is the area of the circle times 2/3rd of the minor axis.

**Example 1:** An ellipsoid whose radius and its axes are a= 21 cm, b= 15 cm and c = 2 cm respectively. Determine the volume for the given ellipsoid.

__Solution:__

Volume of ellipsoid:

*V = 4/3 **× π** **× a** **× b** **× c*

*V = **4/3 **× π** **× 21** **× 15** **× 2*

*V = 2640 cm*^{3}

**Example 2:** The ellipsoid whose radii are given as r_{1} = 9 cm, r_{2} = 6 cm and r_{3} = 3 cm. Find the volume of ellipsoid.

__Solution__:

Radius (r_{1}) = 9 cm

Radius (r_{2}) = 6 cm

Radius (r_{3}) = 3 cm

The volume of the ellipsoid:

*V =** 4/3 **× π** **× r*_{1}* **× r*_{2}* **× r*_{3}

*V = 4/3** **× π** **× 9** **× 6** **×3*

*V = 678.24 cm*^{3}

Volume of ellipsoid (V) = 678.24 cubic units

**Example 3:** An ellipsoid whose radii are given as r_{1} = 12 cm, r_{2} = 10 cm and r_{3} = 9 cm. Find the volume of the ellipsoid.

__Solution__:

Radius (r_{1}) = 12 cm

Radius (r_{2}) = 10 cm

Radius (r_{3}) = 9 cm

The volume of the ellipsoid:

*V =** 4/3 **× π** **× r*_{1}* **× r*_{2}* **× r*_{3}

*V = 4/3** **× π** **× 12** **× 10** **×9*

*V = 4521.6 cm*^{3}

Online Volume Calculator, click on the link will open a new window.