Question

A solid has a circular base and cross sections perpendicular to the base are squares. What method should be used to find the volume of the solid?

   A solid has a circular base and cross sections perpendicular to the base are squares. What method should be used to find the volume of the solid?

Calculus for Scientists and Engineers: Early Transcendental

Calculus for Scientists and Engineers: Early Transcendental

William Briggs, Lyle… 1st Edition

Chapter 6, Problem 6

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Solved by Expert Adnan Gill

06/16/2020

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It has a circular base and cross sections perpendicular to the base are squares. This means that if we cut the solid perpendicular to the base, each piece would be a square. Show more…

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A solid has a circular base and cross sections perpendicular to the base are squares. What method should be used to find the volume of the solid?

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Key Concepts

Definite Integration of Cross Sections

In finding the volume of a solid with known cross-sectional shapes, you express the area of each cross section in terms of a variable that corresponds to its position along the slicing axis. By setting up and evaluating an integral of this area function over the interval that spans the solid, you determine the overall volume of the solid.

Method of Slicing

The method of slicing involves cutting a solid into many thin slices perpendicular to one axis, determining the area of each slice as a function of its position along that axis, and then integrating these areas over the range of the solid. This technique allows you to compute the total volume by summing up the volumes of the infinitesimally thin slices.

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