10.1 The Geometry of Solids/10.2 Volume of Prisms and Cylinders
Polyhedron – A solid whose surface consists of polygons and their interiors
Faces of a polyhedron – The polygons and their interiors that form the polyhedron
Edges of a polyhedron – The line segments where two faces of the polyhedron intersect
Vertex of a polyhedron – A point of intersection of three or more edges of the polyhedron
Tetrahedron – A polyhedron with four faces. The regular tetrahedron is one of the Platonic solids.
Regular polyhedron – A polyhedron whose faces are enclosed by congruent, regular polygons that
meet at all vertices in the same way.
Prism – A polyhedron with two congruent polygons in parallel planes as bases. Line segments (lateral
edges) connect the corresponding bases to form lateral faces, which are parallelograms.
Rectangular
Prism
Triangular
Prism
Hexagonal
Prism
Bases of a prism – The two congruent polygon sides of the prism that are in parallel planes.
Lateral faces of a prism – Faces that are not bases of the prim.
Lateral edges of a prism – The intersection of two lateral faces of the prism.
Right prism – A prism in which the lateral edges are perpendicular to the bases.
Oblique prism – A prism in which the lateral edges are not perpendicular to the bases.
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Altitude of a prism – A line segment between, and perpendicular to, the planes of the bases.
Height of a prism – The length of the altitude of the prism.
Pyramid – A polyhedron with a polygon base and line segments connecting the vertices of the base
with a single point (the vertex of the pyramid) that is not coplanar with the base. The altitude is the
line segment from the vertex ending at and perpendicular to the plane of the base. The height is the
length of the altitude. If the line segment connecting the vertex to the center of the base is
perpendicular to the base, then the pyramid is right, otherwise it is oblique.
Hexagonal
Pyramid
Triangular
Pyramid
Square
Pyramid
Sphere – The set of all points in space at a given distance (the radius) from a given point (the center).
Sphere
Hemisphere
Hemisphere – Half of a sphere including a great circle as its base.
Great circle – The intersection of a sphere with a plane that passes through its center.
Cylinder – A solid whose surfaces consists of all points on two circles in parallel planes, along with
points in their interiors (the bases of the cylinder), and all points on segments joining the two circles.
An altitude of a cylinder is a line segment between and perpendicular to the planes of the bases. The
height of a cylinder is the length of an altitude.
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Axis of a cylinder – The line segment that joins the centers of the bases of the cylinder.
Radius of a cylinder – The radius of a base of the cylinder.
Right cylinder – A cylinder in which the axis is perpendicular to the bases.
Oblique cylinder – A cylinder in which the axis is not perpendicular to the bases.
Cone – A solid whose surface consists of a circle and its interior, and all points on line segments that
connect points on the circle to a single point (the cone’s vertex) that is not coplanar with the circle.
The circle and its interior form the bases of the cone. The radius of the cone is the radius of the base.
The altitude of a cone is the line segment from the vertex to the plane of the base and perpendicular
to it. The height of the cone is the length of its altitude.
Right cone – A cone in which the line segment connecting the vertex of a cone with the center of its
base is perpendicular to the base.
Oblique cone – – A cone in which the line segment connecting the vertex of a cone with the center of
its base is not perpendicular to the base.
Prism-Cylinder Volume Conjecture
The volume of a prism or a cylinder is the area of the base, B, multiplied by the height, h.
__________
Oblique Prism-Cylinder Volume Conjecture
The volume of an oblique prism or cylinder is the same as the volume of a __________ prism or
cylinder that has the same base area and the same height.
Rectangular Prism Volume Conjecture
The volume of a rectangular prism can be found by multiplying the length, l, by the width, w, and the
height, h. ___________
h
w
l
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Cylinder Volume Conjecture
The volume of a cylinder can be found by multiplying  by the square of the radius, r, and the height,
h. ______________
h
r
Example 1: Find the volume of each prism.
a)
b)
6 ft
6 ft
8 ft
c)
d)
4 in
9 in
5 in
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Example 2: Find the volume of each cylinder
a)
b)
7 in
6 in
Example 3: Three right rectangular pie boxes are stacked as shown in the diagram. Find the volume
of the entire stack if all the prism bases are squares.
a)
b)
3 in
3 in
12 in
3 in
34 in
44 in
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Example 4:
a)
b)
4m
6m
5m
14 m
6m
Example 5:
a)
b)
HOMEWORK: Page 509 #10 – 22; Page 517 – 518 #1 - 7
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