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