Please review
Measurements first.
Volume refers to how much space is taken by some
object.
If the length is 12 cm, the width is 10 cm and the
height is 6 cm, then the volume of this box would be (12)(10)(6) = 720 cm3.
If the radius of bowling ball is 6 inches,
then its volume would be (4/3)(3.14)(6)3
= 904 in3.
A right circular cylinder is a cylinder
that has circular ends and the wall is
perpendicular to both of these ends.
If the height of this cone is 12 in, and
the diameter of its base is 8 inches, it's
volume would be (3.14)(42)(12)/3
= 201 in3
If the radius of this cylinder is 1.5 m
and it's height is 3 m then its volume is
(3.14)(1.52)(3) = 21.2 m3.
The difference between these pyramids is
one has a rectangular base while the other
has a triangular base. In either
case to find the area, first the area of
the base must be determined, then the
volume can be calculated.
Suppose the length of a pyramid's
base is 4 in and its width is 6 inches,
and its height is 12 inches, what is its
volume? (4)(6)(12)/3 = 96 in3
Suppose the triangular base of a pyramid
has a side equal to 10 inches and a height
from that side to the opposite vertex of
16 inches and the pyramid's height is 24
inches, what is it's volume?
The area of the base is (1/2)(10)(16) =
80, so (80)(24)/3 = 640 in3.
In the following three figures we can see
the relationships between the areas of the
right circular cylinders to spheres and
cones, and the relationship between a
pyramid to its enclosing box.
If the radius of the sphere is equal to
the radius of the cylinder and height of
the cylinder, then it's 2/3 the volume of
the cylinder.
If the radius of the base of the cone is
equal to the radius of the base of the
cylinder and the height of the cone is
equal to the height of the cylinder
than the volume of the cone us 1/3 the
volume of the cylinder.
Finally, if the base of the pyramid is
identical to the base of the box, and the
height of the pyramid is equal to the
height of the box, then the volume of the
pyramid is equal to 1/3 the volume of the
box, a triangular pyramid will have
a three sided box whose bottom would be
identical to the bottom of the pyramid.
( \a triangular pyramid would have a three
sided box).
This is another FREE ALGEBRA PRINTABLE presented to you from the
Algebra section of
K12math.com