State the Cavalieri's principles for 3D solid objects. Prove that the area of a sector with angle 0 of a circle of radius r is r²e. A solid object has height r. The section by a plane parallel to the base and height h always has the area (r – h)²0. Prove that the volume of the object is r0. (Hint: Compare this solid object with a cone having a sector base as in part b)

State the Cavalieri's principles for 3D solid objects. Prove that the area of a sector with angle 0 of a circle of radius r is r²e. A solid object has height r. The section by a plane parallel to the base and height h always has the area (r – h)²0. Prove that the volume of the object is r0. (Hint: Compare this solid object with a cone having a sector base as in part b)

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

Section9.1: Prisms, Area And Volume

Problem 17E: For the right triangular prism found in Exercise 16, suppose that the sides of the triangular base...

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