Volume Paraboloid

Paraboloid is defined as one of the most important mathematical shape. Paraboloid has three dimension shape. Paraboloid is defined as the combination of ellipse and parabola.  All the sections present in the paraboloid parallel to one coordinate plane is parabola and all the sections present in paraboloid parallel to one coordinate is ellipse. In this section, we are going to see about the volume of paraboloid in detail.
Explanation to Volume Paraboloid

The explanation to volume of paraboloid is given below the following section,

Formula:

Volume of paraboloid = `1/2` `Pi` a2 h

where,

h = height of the paraboloid

Example Problem to Volume Paraboloid

Problem 1: Find the volume of paraboloid, where, h = 10, a = 5.

Solution:

Step 1: The given values for finding the volume of paraboloid is as follows,

h = 10,

a = 5.

Step 2: To find:

Volume of Paraboloid

Step 3:The formula given for finding the volume of paraboloid is as follows,

Volume of Paraboloid = `1/2` `Pi` a2 h

Step 4: By substituting the values in the volume formula,

Volume of Paraboloid = `1/2` `Pi` a2 h

= `1/2` (3.14) (52 ) (10)

= `1/2` (3.14) (25) (10)

= `1/2` (3.14) (250)

=  `1/2` (3.14) (250)

= `1/2` (785)

= 392.5

Result: Volume of paraboloid = 392.5

Thus, this is the require answer for solving the volume of paraboloid.

Problem 2: Find the volume of paraboloid, where, h = 15, a = 6.

Solution:

Step 1: The given values for finding the volume of paraboloid is as follows,

h = 15,

a = 6.

Step 2: To find:

Volume of Paraboloid

Step 3:The formula given for finding the volume of paraboloid is as follows,

Volume of Paraboloid = `1/2` `Pi` a2 h

Step 4: By substituting the values in the volume formula,

Volume of Paraboloid = `1/2` `Pi` a2 h

= `1/2` (3.14) (62 ) (15)

= `1/2` (3.14) (36) (15)

= `1/2` (3.14) (540)

= `1/2` (1695.6)

= 847.8

Result: Volume of paraboloid = 847.8

Thus, this is the require answer for solving the volume of paraboloid.