FINDING VOLUME AND SURFACE AREA THROUGH INTEGRALS

This article explains how to compute volumes and surface areas of three dimensional solids using definite integrals. The focus is on the geometric ideas behind slicing, accumulation, and revolving curves around an axis, rather than on memorizing formulas. Core methods include the disk and washer approach, the cylindrical shell approach, and surface area integrals for surfaces of revolution.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-02-01
DOI
https://doi.org/10.5281/zenodo.18448537
Primary Topic
Advanced Theoretical and Applied Studies in Material Sciences and Geometry
Type
article
Field-Weighted Citation Impact
0.00
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article

FINDING VOLUME AND SURFACE AREA THROUGH INTEGRALS

Sardorkhuja Mansurkhujaev, Azizkhuja Mansurkhujaev
Zenodo (CERN European Organization for Nuclear Research)
Advanced Theoretical and Applied Studies in Material Sciences and Geometry
article

FINDING VOLUME AND SURFACE AREA THROUGH INTEGRALS

Sardorkhuja Mansurkhujaev, Azizkhuja Mansurkhujaev
article en

Abstract

This article explains how to compute volumes and surface areas of three dimensional solids using definite integrals. The focus is on the geometric ideas behind slicing, accumulation, and revolving curves around an axis, rather than on memorizing formulas. Core methods include the disk and washer approach, the cylindrical shell approach, and surface area integrals for surfaces of revolution.

Zenodo (CERN European Organization for Nuclear Research)
Tashkent State University of Economics (UZ)
Sustainable cities and communities
Openalex Percentile: Top 71%
Advanced Theoretical and Applied Studies in Material Sciences and Geometry
DOIOpen Access PDFOpenAlex
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