Page 21 - AG Unit 2 Capacity, Cavalieri, and Constructions

Pre-scribed
AG 2.6 Volume and Rotation Problems* Geometry

Name ______________________ 7. A rectangle has a length of 3 m and a height of
Class _____ Date ____ 5 m. What is the volume of the cylinder made by
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1.Given a sphere with a volume of 2000 cm , find rotating this rectangle along an edge? Is the
the area of the cross section through its center. volume the same despite which edge?

2. Given a cylinder with a radius of 7 cm and a 8. An isosceles triangle has base of 20 ft and an
height of 10 cm, find the area of the cross- altitude of 30 ft. What is the volume of the cone
section that is parallel to its base. made by rotating this triangle along its altitude?

3. Given a cone with a radius of 6 ft and a height 9. A square with area of 100 cm is rotated
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of 12 feet, find the area of the triangle formed by along its center to form a cylinder. What is the
a perpendicular cross-section down through the volume of the cylinder?

cone’s center.

10. If an equilateral triangle with perimeter 24 cm
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4. Given a cube with a volume of 27,000 cm , is rotated, find the volume of the cone that is
find the area of a cross-section parallel to its formed along its altitude.
base.

5. A cylinder has a height of 60 mm and radius of Smarter Problems:

20 mm. Find the area of the rectangle formed by 13. Remember any basic trigonometry? Can you
the perpendicular cross-section right down the give the volume of the
cylinder’s center. water being held in the
prism below?

6. A circle has a radius of 15 cm. What is the
volume of the sphere made by rotating this circle
about its center?

From shmoop online