10.4Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres
1. Which identifies the figure?
A rectangular pyramid
B rectangular prism
C cube
D square pyramid
2. What best describes the cross section
shown on the cube?
A square C trapezoidB triangle D rectangle
3. A polyhedron has 7 vertices and 12
edges. Which number of faces justifies
Eulers formula?
A 3 C 17
B 7 D 21
4. In the figure, which number
should be substituted for
V in Eulers formula?
A 6 C 12B 8 D 18
10.4 Day 1 Warm-up
10.4Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres
PRISM: polyhedron with _____congruent faces,
called bases, that lie in ____________ planes.
(Prisms are classified by the shapes of their ______.)
The other faces, called lateral faces, are
parallelograms formed by connecting the
corresponding vertices of the bases.
The segments connecting these vertices are
lateral edges.
o Right prism: each lateral edge is ______________ to both bases.
o Oblique prism: the lateral edges are not ______________to the bases.
two
parallel
bases
perpendicular
perpendicular
Lateral Area of a Prism: ______ of the ______ of the lateral faces
SURFACE AREA of a Right Prism: sum of the areas of the two bases
and the lateral area
___.___. = ____ + ____ (B = area of a base, P = perimeter of a base,
h = height of the prism)
sum areas
S.A. 2B Ph
Find the surface area of the right prism.
1. 2.
5 m
12 m
CYLINDER: solid with__________ ________ bases that lie in ________
planes.
o Right Cylinder: if the segment joining the ________
of the bases is perpendicular to the bases.
congruent circular parallel
centers
Lateral Area of a Cylinder: the area of its ____________ surface.
SURFACE AREA of a Right Cylinder: sum of the areas of the
two bases and the lateral area
S.A. = ____ + ____ (B = area of a base, C = circumference of a
base, h = height of the cylinder)
S.A. = ______ + ______ (r = radius of a base)
curved
2B Ch
2r2 2rh
Find the surface area of the right cylinder.
3. 4.
10.4 Day 2 Warm UpWrite a description of each figure.
1. cube
2. pentagonal prism
3. cylinder
prism with 6 square faces
prism with 2 pentagonal bases and 5 lateral faces that are parallelograms
figure with 2 circular bases connected by a curved surface
PYRAMID: polyhedron in which the base is a ______________
and the lateral faces are __________ with a common vertex.
(Pyramids are classified by the shape of their ________.)
The intersection of two ________ __________ is a lateral edge.
The intersection of the _________ and a _______ _____ is a base edge.
The altitude or height of the pyramid is the _____________
____________ between the __________ and the____________.
o Regular pyramid: has a regular ___________
for a base and its height meets the base at its
_________.
The slant height of a regular pyramid is the
___________ of _______ lateral face.
polygon
trianglesbases
lateral faces base lateral face
base vertex
perpendicular
distancepolygon
center
anyaltitude
SURFACE AREA of a Regular Pyramid:
S.A. = ___ + __ ____(B = area of the base, P = perimeter of the base, l = slant height)
B Pl
Find the surface area of the regular pyramid.
1. 2.
CONE: has a ________ base and a vertex that is ______ in the same ________ as the base.The altitude or height is the perpendicular ____________between the _________ and the __________.The lateral surface of a cone consists of all ___________ that connect the ___________ with the points on the base edge.
Right Cone: the height meets the base at its _____________.The slant height is the distance between the _________ and ____ point of the base edge.
circular not
plane
distance
vertex basesegments
vertex
center
vertex a
SURFACE AREA of a Right Cone:
S.A. = __ + __ _____(B = area of the base, C = circumference of the base, l = slant height)
S.A. = _____ + ____
(r = radius of the base, l = slant height)
B Cl
r2 rl
Find the surface area of the right cone.
3. 4.
SPHERE: the _________of points in space that are a given
distance from a ________.
The point is called the center of the sphere.
A radius of a sphere is a segment from the _______ to ___
_______on the sphere.
A great circle is the _____ _______ of a
sphere with a ______ that goes through the
center of the sphere.
Every great circle of a sphere separates the
sphere into two ________ _______ called
hemispheres.
SURFACE AREA OF A SPHERE:
S.A. = ______ (r = radius of the sphere)
locus
point
a
point
center
cross sectionplane
congruent halves
4r2
Find the surface area of the sphere.
1. 2. 3.
All spheres are similar to each other. Use problems 1 and 2 above to answer the following.
What is the ratio of their radii?
Add to your notes
1. 2.
What is the ratio of their surface areas?
Given two spheres have radii with a ratio of
, what is the ratio of their surface areas?
