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Find the volume of the solid generated by revolving the region about the given line?

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Alice's magical spinning table creates a cylinder when twirled. The volume is found with the formula V = πr²h, resulting in approximately 113,097 cubic units for a table with a 33-unit radius.

When Alice spins her flat circular table, the solid formed is a cylinder. To calculate the volume of the cylinder, we use the formula for the volume of a cylinder, V = πr²h, where r is the radius and h is the height. Since the radius of the circular table is given as 33 units and the height would be the same as the radius when it is spun around a central axis, we can plug the values into our formula.

Thus, the volume V is V = π(33)^2(33) = π(33)^3. Now, we calculate:

V = π(35,937) = approximately 113,097 cubic units (since π is approximately 3.14159).

This whimsical solid, therefore, would have an impressive volume of around 113,097 cubic units, enough to bring wonder to Alice's tea party guests!

The probable question may be:

Imagine a delightful tea party in Wonderland where Alice is arranging cupcakes on her magical spinning table. The table is a flat circular region with a radius of 33 units. Now, if Alice decides to twirl the table around a mystical axis, creating a whimsical solid shape, what would be the volume of this enchanting solid?

Additional Information:

Alice, being an excellent hostess, loves to create unique tea party settings. The table, resembling a colorful tea saucer, has a radius of 33 units, perfect for accommodating her Wonderland friends. Now, envision the table spinning around a mysterious axis, forming a three-dimensional shape with an intriguing volume. To calculate this volume, think of the joyous tea party atmosphere and the magical essence infused into this whimsical solid.

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