Download 9-1C Surface Area of Cylinders and Cones - Winterrowd-math

9-1C Surface Area of
Cylinders and Cones
What are the parts of a cylinder?
What is the formula for the lateral area of a
cylinder?
What is the formula for the surface area of a
cylinder?
What are the parts of a cone?
What is the formula for the lateral area of a cone?
What is the formula for the surface area of a
cone?
Parts of a Cylinder
A cylinder has two congruent circular bases
in parallel planes.
The axis of a cylinder is the segment that
joins the centers of the bases.
Right cylinder—the axis is perpendicular to
the base.
An altitude of a cylinder is a segment that
joins the planes of the bases and is
perpendicular to them.
The height of a cylinder is the length of the
altitude.
Parts of a Cylinder
radius
altitude
axis
right cylinder
Right or Oblique?
Lateral Area—Can Labels
What does the lateral
area of a cylinder
look like when it is
flattened out?
Lateral Area of Cylinders
The lateral area of a right cylinder is the
product of the circumference of its base
and the height of the cylinder.
LA = 2πrH
Radius (r)
Height (H)
Surface Area of a Cylinder
The surface area of a right cylinder is the
sum of its lateral area and the areas of its
bases.
SA = 2πrH + 2πr2
Radius (r)
Height (H)
Find the lateral area and the
surface area of the right cylinder.
LA = 2πrH
LA = 2π(8)(4)
LA = 201.1 in2
8 in
4 in
SA = 2πrH + 2πr2
SA = 2π(8)(4) + 2π(8)2
SA = 603.2 in2
Find the lateral area and the
surface area of the right cylinder.
C = 18π (2πr)
LA = 2πrH
LA = 18π(14)
LA = 791.7 cm2
SA = 2πrH + 2πr2
SA = 791.7 + 2π(14)2
SA = 1300.6 cm2
14 cm
Parts of a Cone
vertex
A cone has a vertex and
a circular base.
slant height (slant)
The axis of a cone is the
segment from the
vertex to the center of
the base.
In a right cone, the axis
is perpendicular to the
base.
axis
height (H)
Right or Oblique?
Lateral Area of Cones
The lateral area of a right cone is one-half
the product of the circumference of its
base and the slant height of the cone.
LA = ½ ·2 ·π r(slant) or
π (r)(slant)
Surface Area of Cones
The surface area of a right cone is the sum of
its lateral area and the area of its base.
SA = π(r)(slant) +πr2
Find the lateral area of a right cone
whose base radius is 4 in and slant
height is 11 in.
LA = π(r)(slant)
LA = π(4)(11)
LA = 44π ≈ 138.2 in2
11 in
4 in
Find the surface area of the cone.
SA = π(r)(s)+πr2
SA = (4)(11)π + π(4)2
SA = 44π + 16π
SA = 60π ≈ 188.5 in2
11 in
4 in
• What are the parts of a cylinder?
Raduis, altitude (height)
• What is the formula for the lateral area of a
cylinder?
LA = 2πrH
• What is the formula for the surface area of a
cylinder?
SA = 2πrH + 2πr2
• What are the parts of a cone?
Radius, slant height
• What is the formula for the lateral area of a cone?
LA = π (r)(slant)
• What is the formula for the surface area of a
cone?
SA = π(r)(slant) +πr2
Assignment 9-1C
Page 617, 1-10,
18-24 even
NO FORMULAS WITH NUMBERS
NO CREDIT