Solids produced by rotating polygons
A rectangle
rotated
about its
edge
produces a
cylinder.
A rectangle
rotated about
its central axis
(contains
midpoints of
both sides)
produces a
cylinder.
A right triangle
rotated about its
leg produces a
cone.
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A triangle
rotated about
its axis of
symmetry
produces a
cone.
A semicircle
rotated about
its diameter
produces a
sphere
A circle rotated
about its diameter
produces a sphere.
1. What’s the surface area of the geometric solid produced by the triangle below when it’s rotated 360 degrees about
the axis AB?
2. Find the volume and the lateral surface area of the geometric solid produced by the rectangle below when it’s
rotated 360 degrees about the axis AB?
3. Find the volume and the surface area of the geometric solid produced by the circle below when it’s rotated 360
degrees about its diameter?
4. What’s the volume of the geometric solid produced by the isosceles triangle below when it’s rotated 360 degrees
about its axis of symmetry?
Geometry WS – Cavalieri’s Principle
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1. Use Cavalieri’s principle to find the volume for each of the following.
2. Find the volume of the oblique hexagonal prism below.
3. Find the volume of an oblique circular cylinder that has a radius of 5 feet and a height of 3 feet. Round to the
nearest tenth.
4. A can 12 centimeters tall fits into a rubberized cylindrical holder that is 11.5 cm tall, including 1 cm for the
thickness of the base of the holder. The thickness of the rim of the holder is 1 cm. What is the volume of the
rubberized material that makes up the holder? Round to the nearest hundredth.
6. If the volume is 360 ft 2, find x.
7. If the volume is 72 cm3, find x.