18 Show that the volume V of a regular tetrahedron, all of whose side lengths are s, is V = 1½³√2 (all fourfaces of a regular tetrahedron are equilateral triangles). Hence find the rate of increase of the surface areawhen the volume is 144√√2 cm³ and is increasing at a rate of 12 cm³/s.

Show that the volume V of a regular tetrahedron with side length s is V=121s32 A regular…

Answered: 18 Show that the volume V of a regular…

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.CR: Review Exercises

Problem 6CR: The base of a right prism is a regular hexagon whose sides are 8cm in length. The height of the...

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18 Show that the volume V of a regular tetrahedron, all of whose side lengths are s, is V = 1½³√2 (all four faces of a regular tetrahedron are equilateral triangles). Hence find the rate of increase of the surface area when the volume is 144√√2 cm³ and is increasing at a rate of 12 cm³/s.