Chapter 16: Surface Area and Volume 225Volume
The volume of a pyramid is one-third of the volume of a prism with the same base and height.
Conveniently, the volume of a cone is one-third of the volume of a cylinder with the same base
and height. For a cone, Vrh^1
3(^2).
To find the volume of a cone 9 meters high with a base that has a radius of 8 meters, follow the
formula.
The volume is 192S cubic meters, or approximately 603.2 cubic meters.
Vrh
V
^1
3
1
3
89
1
3
64 9 192
2
2
CHECK POINT
Find the surface area and volume of each cone. SA = Sr^2 + Srl and V =^13 Sr^2 h
- A cone with radius 10 cm, height 24 cm, and slant height 26 cm.
- A cone with diameter 8 inches, height 3 inches, and slant height 5 inches.
- A cone with circumference 16S cm, height 6 cm, and slant height 10 cm.
- A cone with radius 12 inches and height 5 inches. (Hint: Use the Pythagorean
theorem to find the slant height.) - A cone with base area 324S cm and a height of 24 cm.
Spheres
The last category of solids is the hardest to define and one you’ve probably known almost all
your life. A sphere is not a polyhedron because it’s not formed from polygons. It’s not a cylinder
because it doesn’t have that lateral area. The sphere is the shape you’d produce if you could
grab a circle by the ends of a diameter and spin it around that diameter so fast it blurred into
something three dimensional. Put another way, it’s a ball.
Officially, a sphere would be defined as the set of all points in space at a fixed distance from a
center point. You can think of it as a 3-D circle, or a ball.