Answered: Question (5): Find the volume of the…

Question (5): Find the volume of the largest right circular cone that can be inscribed in a sphere of radius 3, as shown in the figure below? 3

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.3: Cylinders And Cones

Problem 13E: Find the volume of the oblique circular cylinder. The axis meets the plane of the base to form a 45...

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Concept explainers

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.

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Step 1: First let us draw the diagram for the given data.

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Step 2: To find the radius of the cone r use Pythagoras theorem to the triangle ODC.

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Step 3: The maximum volume of the right circular cone is given by

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Step 4: calculate the critical points by differentiating the above equation and equating it to 0.

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Step 5: calculate the volume by substituting the above values.

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