SimilarSolids
LearningObjectives
- Find the volumesof solidswith basesof equalareas.
Introduction
You’velearnedformulasfor calculatingthe volumeof differenttypesof solids—prisms,pyramids,cylinders,
and spheres.In mostcases,the formulasprovidedhad specialconditions.For example,the formulafor the
volumeof a cylinderwas specificfor arightcylinder.
Now the questionarises:Whathappenswhenyou considerthe volumeof two cylindersthat havean equal
basebut one cylinderis non-right—thatis, oblique.Doesan obliquecylinderhavethe samevolumeas a
right cylinderif the two sharebasesof the samearea?
Partsof a Solid
Given,two cylinderswith the sameheightand radius.One cylinderis a right cylinder, the otheris oblique.
To see if the volumeof the obliquecylinderis equivalentto the volumeof the right cylinder, first observethe
two solids.
Sincethey both havethe samecircularradius,they both havecongruentbaseswith area:
Now cut the right cylinderinto a seriesof cross-sectiondiskseachwith height and radius.