Section 12.4 ~Volume of Prisms and Cylinders
Topics in this lesson:
• volume of prism/cylinder
• Cavalieri's Principle
Objective: To be able to find the volume
of prisms and cylinders.
Vocabulary
volume ­ the number of cubic units contained in the interior of a solid
Volume of a Prism
The volume V of a prism is:
V = B = base
h = height
Volume of a Cylinder
The volume V of a cylinder is:
V = Example 1 ­ Find the volume of the solid.
a) right triangular prism b) right cylinder
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Example 2
The volume of the right cylinder shown is 1253 cubic centimeters. Find the value of x.
Example 3
The volume of the right cylinder is 200π cubic centimeters. Find the value of x.
Cavalieri's Principle
If two solids have the same height and the same cross­sectional area at every level, then they have the same volume.
*This tells us that the formulas for volume of a right prism and cylinder work on oblique prisms and cylinders. However, this is not the case for surface area. Example 4 ­ Find the volume of the oblique cylinder. Example 5 ­ Find the volume of the solid.
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