Video: Applying Cavalieri’s Principle

A right circular cylinder and an oblique circular cylinder have the same radius and height, as seen in the given figure. What does Cavalieri’s principle tell us about the volume of the two shapes? Work out the volume of the oblique cylinder. Give your answer in terms of 𝜋.

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Video Transcript

A right circular cylinder and an oblique circular cylinder have the same radius and height as seen in the given figure. What does Cavalieri’s principle tell us about the volume of the two shapes? Then work out the volume of the oblique cylinder. Give your answer in terms of 𝜋.

Cavalieri’s principle tells us that if the cross sections of the figure have equal areas at all spaces and the altitude of both the solids are the same, then the volumes are equal. To work out the volume of the oblique cylinder, we only have to work out the volume of the right cylinder.

The volume of a right cylinder is equal to 𝜋 times the radius squared times the height of the cylinder. For us, that’s 𝜋 times one squared times five. We’re leaving everything in terms of 𝜋, so we don’t need to estimate that. One squared is one, times five. One times five equals five. And we aren’t getting rid of the 𝜋.

So we’ll leave it as five 𝜋. The volume of both of the cylinders in this image is five 𝜋.

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