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12.4 volume of prisms and cylinders

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Jessica Garcia
Jessica Garcia

This document discusses calculating volumes of prisms and cylinders. It provides examples of using the volume formulas of prisms (V=Bh) and cylinders (V=πr^2h) to find volumes. It also explains Cavalieri's principle, which states that solids with equal heights and cross-sectional areas have the same volume.

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12.4 Volume of Prisms & Cylinders Geometry
Objectives/Assignment ,[object Object],[object Object]
Exploring Volume ,[object Object]
Volume Postulates ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Ex. 1: Finding the Volume of a rectangular prism ,[object Object]
Ex. 1: Finding the Volume of a rectangular prism ,[object Object]
Conclusion ,[object Object],[object Object]
Note: ,[object Object]
Finding Volumes of prisms and cylinders. ,[object Object]
Cavalieri’s Principle ,[object Object]
Volume Theorems ,[object Object],[object Object]
Ex. 2: Finding Volumes ,[object Object],V = Bh Volume of a prism formula A = ½ bh Area of a triangle A = ½ (3)(4) Substitute values A = 6 cm 2 Multiply values -- base V = (6)(2) Substitute values V = 12 cm 3 Multiply values & solve
Ex. 2: Finding Volumes ,[object Object],V = Bh Volume of a prism formula A =  r 2 Area of a circle A =  8 2 Substitute values A = 64  in. 2 Multiply values -- base V = 64  (6) Substitute values V = 384  in. 3 Multiply values & solve V = 1206.37 in. 3 Simplify
Ex. 3: Using Volumes ,[object Object]
Ex. 3: Using Volumes ,[object Object]
Ex. 4: Using Volumes in Real Life ,[object Object]
Ex. 4: Using Volumes in Real Life ,[object Object],[object Object],[object Object], To find the weight of the block, multiply the pounds per cubic foot, 145 lb/ft. 3 by the number of cubic feet, 0.40 ft 3 . Weight = 145 lb 1 ft 3 • 0.40 ft 3  58 lbs.

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12.4 volume of prisms and cylinders

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