Page 22 - AG Unit 2 Capacity, Cavalieri, and Constructions

AG 2.7 B Volume and Rotation Problems*

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
3
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
2
9. A square with area of 100 cm is rotated
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
3
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