Transcript lateral area

Get started on your warm-up!
Ramona has a cake pan shaped like half of a
sphere. Describe the shape of the cross sections
of cakes baked in this pan if they are cut
horizontally and vertically.
Warm-Up
Notes on Surface
Areas of Prisms and
Cylinders
Apply geometric methods to solve problems (e.g.,
designing an object or structure to satisfy physical
G.MG.3
constraints or minimize cost; working with typographic
grid systems based on ratios).
• Find lateral areas of surface areas of prisms.
• Find lateral areas and surface areas of cylinders.
Did you know?
Atlanta’s Georgia Aquarium is the largest aquarium in
the world, with more than 8 million gallons of water
and more than 500 species from around the world.
The aquarium has an underwater tunnel that is 100
feet long with 4574 square feet of viewing windows.
Think-Pair-Share
• What is the shape of the underwater tunnel?
• If you are given the area and length of a
surface, how can you find its width?
• How could you find the length of the
semicircle of the tunnel?
Lateral Areas and Surfaces Areas of
Prisms
• Faces that are not bases are called lateral faces.
• Lateral faces intersect each other at the lateral edges
which are parallel and congruent.
• Lateral faces intersect the base at the base edges.
• The perpendicular segment that joins the planes of the
bases.
• The height is the length of the altitude.
Lateral Area
• The lateral area L of a prism is the sum of the
areas of the lateral faces.
In general, the lateral area of a prism
can be found using…
L=Ph
Example #1
Find the lateral area of the prism.
Surface Area of a Prism
• The surface area of a prism can be found
using…
Surface Area of A Cylinder
• The axis of a cylinder is the segment with
endpoints that are the centers of the circular
bases.
• A right cylinder has the axis as the altitude, an
oblique cylinder does not.
Lateral Area and Surface Area of Right
Cylinders
• The lateral area of a right cylinder is the area
of the curved surface and it can be found
using this equation:
L=2𝝅rh
• The surface area of a right cylinder is S=2𝝅rh+
2𝝅r2 where r is the radius of a base and h is
height
Example #2
• Find the lateral area and the surface area of
the cylinder. Round to the nearest tenth.
Did you know?
The Transamerica
Pyramid in San
Francisco, California,
covers nearly one
city block. Its
unconventional
design allows light
and air to filter down
to the streets around
the building, unlike
the more traditional
rectangular prism
skyscrapers.
Think-Pair-Share
• What is the general shape of the building?
• How does the design allow more light to reach
the street?
• What is a possible disadvantage of a building
of this shape?
Lateral Area and Surface Area of
Pyramids
• A regular pyramid has a base that is a regular
polygon and the altitude has an endpoint at
the center of the base.
• The lateral faces are congruent isosceles
triangles.
• The height of each lateral face is called the
slant height of the pyramid.
Lateral Area of a Pyramid
1
L= P𝑙
2
• The lateral area of a regular pyramid is
where P is the perimeter of the base and l is
the slant height.
Example #1
Find the lateral area of the square pyramid.
Surface Area of a Regular Pyramid
• The surface area of a regular pyramid is
1
S= 𝑃𝑙 + 𝐵 where P is perimeter of the base, l
2
is slant height, B is area of the base.
Example #2
• Find the surface area of the square pyramid.
Lateral Area of a Cone
• The lateral area of a cone can be found using
L=𝝅rl , where r is the radius of the base and
l is the slant height.
Surface Area of a Cone
• The surface area S of a right circular cone is S=
𝝅rl + 𝝅r2 where r is the radius of the base
and l is the slant height.
Example #3
• Find the surface area of the cone. Round to
the nearest tenth.
Practice
• Find the surface area and lateral area of the
Birthday Hat at your table.
• Once you’ve found this, complete the
pyramids of Giza activity.
Great Pyramid of Giza
• Using the following
dimensions of this
pyramid, can you find
the surface area?
• Slant Height: 480.69
feet
• Length of Sides: 434
feet