Derive and apply the formula for finding the volume of prisms and cylinders, being sure to discuss units.
Provide practice examples solving for the volume of prisms and cylinders, reviewing how to report answers in terms of pi () for cylinders
This packet should help a learner seeking to understand how to find the volume of prisms and cylinders.
This video explains how to find the volume of a cube.
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This video explains how to find the volume of a rectangular prism.
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This video explains how to find the volume of prisms other than right rectangular prisms.
This video explains how to find the volume of a right circular cylinder.
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Once one understands how to find the volume of a prism, the derivation of the volume of a cylinder is fairly trivial. Cylinders are, essentially, just prisms with a circular base, so finding the volume of a cylinder is just like finding the volume of a cylinder.
The formula for the volume of a prism is V = B * h, where V is volume, B is the area of the base, and h is the height of the prism. The base of a cylinder is a circle, which has area πr^{2}. Height, obviously, is the same in a cylinder as it is in a prism. By substituting πr^{2} for B in the formula for the volume of a prism, we arrive at the formula for the volume of a cylinder:
V = πr^{2}h.
This video explains how to find the volume of an oblique circular cylinder.
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