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KB20448609: Using TINKERCAD to change a cone to a cylinder

Summary

This short video demonstrates how to transform the properties of a shape in TINKERCAD, from a cone to a cylinder. It also provides an example of how the formula for a frustum can be used to also represent a cone or a cylinder.

Video

More information

We begin with the formula for calculating the volume of a conical frustum:

\[V_{frustum} = {\pi h \over 3}{(R^2 + Rr + r^2)}\]

The height h and the base radius R remain constant in this video demonstration. The only property of the shape that we change is the top radius r.

We can re-write this formula as a function with one variable (the top radius):

\[f(r) = {\pi h \over 3}{(R^2 + Rr + r^2)}\]

In this function, we can set the top radius to equal the base radius (that is, if r = R). In this case, the base radius is the input for the function:

\[f(R) = {\pi h \over 3}{(R^2 + R \cdot R + R^2)}\]

Once we have substituted the value, we can simplify the expression.

First, we group the like terms:

\[f(R) = {\pi h \over 3}{(R^2 + R^2 + R^2)}\] \[f(R) = {\pi h \over 3}{(3 \cdot R^2)}\]

Next, we simplify the coefficients:

\[f(R) = {\pi h \over \not{3}}{(\not{3} \cdot R^2)}\] \[f(R) = {\pi h R^2}\]

Then, we can also re-arrange the expression for clarity:

\[f(R) = {\pi R^2 h}\]

In summary, when the top radius is equal to the base radius (r = R), we have the formula for the volume of a cylinder.

\[V = {\pi R^2 h}\]

QUESTION

What happens when we set the top radius equal to zero (r = 0)? Show your work.




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