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Explain why the volume of the oblique prism below, which has the same base and height as the previous right prism above, is also V = Bh. Make reference to a principle discussed in class, and explain why that principle is true. %3D oblique prism height is an altitude outside the prism

Explain why the volume of the oblique prism below, which has the same base and height as the previous right prism above, is also V = Bh. Make reference to a principle discussed in class, and explain why that principle is true. %3D oblique prism height is an altitude outside the prism

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter63: Volumes Of Pyramids And Cones
Section: Chapter Questions
Problem 8A
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31. Mastery Objective 31:Explain why V = Bh for both right and oblique prisms, including application of Cavalieri's Principle; explain why Cavalieri's Principle does not apply to surface area. (a) Explain why the volume V of of the right prism shown below is V = Bh, where B is the area of a base and h is the height of the prism. Be sure to keep units throughout your explanation and conclusion, and be sure to address the operation of multiplication. BIS The Arco of a base h is the night Tet Say Aten is BCm?) and height IS h h meters, Let's divide Prism into nequa l parts? by Slicing it ross-sectionally The height Ofindividul Slice would be hin meters teant= h meters Volue of this slice Area -Bcm²) Basexhegt right prism height is a lateral edge There are total nsilce of westack them on owe eacn Other The new solid Will 10ok Tike the onfé co the volume will sumo2o lumes of we cut slices erom. Caan Slice, V=Bxh +Bth +. + Bxh [ntimes] =BX hX V= Bxh Cmoy (b) Explain why the volume of the oblique prism below, which has the same base and height as the previous right prism above, is also V = Bh. Make reference to a principle discussed in class, and lain that pri is rue. oblique prism height is an altitude outside the prism (c) Explain that, while the two prisms above have the same volume, they do not have the same area. Why is this? Be specific.
Transcribed Image Text:31. Mastery Objective 31:Explain why V = Bh for both right and oblique prisms, including application of Cavalieri's Principle; explain why Cavalieri's Principle does not apply to surface area. (a) Explain why the volume V of of the right prism shown below is V = Bh, where B is the area of a base and h is the height of the prism. Be sure to keep units throughout your explanation and conclusion, and be sure to address the operation of multiplication. BIS The Arco of a base h is the night Tet Say Aten is BCm?) and height IS h h meters, Let's divide Prism into nequa l parts? by Slicing it ross-sectionally The height Ofindividul Slice would be hin meters teant= h meters Volue of this slice Area -Bcm²) Basexhegt right prism height is a lateral edge There are total nsilce of westack them on owe eacn Other The new solid Will 10ok Tike the onfé co the volume will sumo2o lumes of we cut slices erom. Caan Slice, V=Bxh +Bth +. + Bxh [ntimes] =BX hX V= Bxh Cmoy (b) Explain why the volume of the oblique prism below, which has the same base and height as the previous right prism above, is also V = Bh. Make reference to a principle discussed in class, and lain that pri is rue. oblique prism height is an altitude outside the prism (c) Explain that, while the two prisms above have the same volume, they do not have the same area. Why is this? Be specific.
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