Application of Double Integral in Calculating the Volume of a Paraboloid-Shaped Pot Using MATLAB

Nurul Wahidah Harahap; Qisti Hafizhah Lubis; Roseyla Sahdina Pasaribu; Tyesa Junika Sihombing

Authors

Nurul Wahidah Harahap State University of Medan
Qisti Hafizhah Lubis State University of Medan
Roseyla Sahdina Pasaribu State University of Medan
Tyesa Junika Sihombing State University of Medan

Keywords:

Double integral, Paraboloid, MATLAB

Abstract

Background:
Double integrals are an important concept in multivariable calculus and are widely applied in calculating the volume of three-dimensional geometric objects with complex shapes. One such object is a paraboloid-shaped cauldron, which is commonly found in engineering and scientific applications. Manual calculations of its volume can be time-consuming and prone to errors.

Objective:
This study aims to apply double integrals to calculate the volume of a paraboloid-shaped cauldron and to validate the analytical results using MATLAB.

Method:
The cauldron is modeled as a symmetric paraboloid represented by the function z=a(x2+y2)z = a(x^2 + y^2)z=a(x2+y2). The volume is calculated analytically using double integrals in polar coordinates to simplify the integration process. Numerical computation is then performed using MATLAB to verify the analytical results.

Results:
The analytical calculation shows that the volume of the paraboloid-shaped cauldron is approximately 31,517 cm³. The numerical results obtained from MATLAB are consistent with the analytical solution and demonstrate higher computational efficiency with reduced rounding errors.

Conclusion:
The results indicate that double integrals in polar coordinates provide an accurate method for calculating the volume of a paraboloid-shaped object. The use of MATLAB effectively supports the analytical approach by improving efficiency and accuracy, making it a reliable tool for volume analysis of complex geometric shapes.

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