Lesson 8.3B
M.3.G.2 Apply, using appropriate units, appropriate formulas (area,
perimeter, surface area, volume) to solve application problems involving
polygons, prisms, pyramids, cones, cylinders, spheres as well as
composite figures, expressing solutions in both exact and approximate
forms
Review
Volume: The number of cubic units needed to fill a
space
Remember, volume is always measured in units cubed
Volume of Pyramids
Volume of a pyramid:
B = Area of the Base
h = height of the pyramid (not the slant height)
Example
Find the volume of the given pyramid.
15 m
16 m
16 m
Example 2
Find the volume of the given pyramid.
8.8 m
4m
Now You Try…
Find the volume of the given pyramid.
21"
10"
24"
Volume of Cones
Volume of a cone: V =
r = radius of the base
h = height of the cone
Example
Find the volume of the cone.
10 cm
12 cm
Now You Try…
Find the volume of the cone.
4 in
11 in
Volume of Spheres
Volume of a sphere:
r = radius of the sphere
Example
Find the volume of the given sphere.
8cm
Word Problems
Dixie cups are cones with a 3 inch height and a 2 inch
radius. How much water fits in one Dixie cup?
Example 2
A spherical ice cream scoop rests on an ice cream cone that is shaped like
a right cone. Suppose the ice cream melts. Will it fit inside the cone?
Justify your answer. (assume that melted and frozen ice cream have
equal volume)
Now You Try…
The top of the Washington Monument in Washington, D.C., consists of a
regular square pyramid with a height of 55 ft. The length of a side of
the base of the pyramid is about 34.4 ft. Find the volume.