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11.2 Notes.notebook

11.2 Notes.notebook
March 28, 2013
11.2 Surface Areas of Prism and Cylinders
base
Notice that the bases are congruent polygons in parallel planes.
base
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11.2 Notes.notebook
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base
altitude
The altitude is the segment joining the two base planes and it is perpendicular to both.
Again, it is called the height, h.
base
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11.2 Notes.notebook
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base
altitude
lateral
face
base
The faces of the prism that are not bases are lateral faces.
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base
altitude
lateral
face
base
lateral
edge
When adjacent lateral faces intersect in parallel segments, they are the lateral edges.
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The lateral faces of prisms are parallelograms.
If they are rectangles, the prism is a right prism.
Otherwise the prism is an oblique prism.
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Oblique pentagonal prism
Right triangular prism
Lateral edges are altitudes.
Right rectangular prism
(Rectangular solid)
Lateral edges are NOT altitudes.
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The surface area of a solid is measured in square units.
The lateral area (L.A.) of a prism is the sum of the areas of its lateral faces.
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The total area (T.A.) of a prism is the sum of the areas of all its faces.
T.A. = L.A. + 2B
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Theorem
The lateral area of a right prism equals the perimeter of a base times the height of the prism.
L.A. = ph
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11.2 Notes.notebook
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h
g
f
e
i
j
d
k
c
a
b
L.A. = ah + bh + ch + dh + eh + fh + gh + ih + jh + kh
L.A. = (a + b + c + d + e + f + g + i + j + k)h
L.A. = (perimeter)h
L.A. = ph
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11.2 Notes.notebook
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What is the surface area of the prism. Use a net.
94 cm2
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11.2 Notes.notebook
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What is the surface area of the triangular prism? Use a net.
216 cm2
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11.2 Notes.notebook
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What is the surface area of the prism?
84 cm2
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11.2 Notes.notebook
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What is the surface area of the prism. Use a net.
220 cm2
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11.2 Notes.notebook
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What is the surface area of the prism?
268.9 in2
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What is the lateral area of the prism?
432 m2
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11.2 Notes.notebook
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What is the area of a base in simplest radical form?
54√3 m2
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11.2 Notes.notebook
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What is the surface area of the prism rounded to a whole number?
619 m2
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11.2 Notes.notebook
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What is the surface area of the prism?
130 in.2
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11.2 Notes.notebook
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What is the surface area of the prism?
(133 + 42√2) ft2 or about 192.3 ft2
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11.2 Notes.notebook
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12 cm
5 cm
4 cm
6 cm
5 cm
A right trapezoidal prism is shown.
Find (a) lateral area
(b) total area
10 cm
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12 cm
5 cm
4 cm
6 cm
5 cm
A right trapezoidal prism is shown.
Find (a) lateral area
(b) total area
10 cm
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11.2 Notes.notebook
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A cylinder is like a prism except that its bases are circles instead of polygons.
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11.2 Notes.notebook
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In a right cylinder, the segment joining the centers of the circular bases is an altitude.
h
The length of an altitude is called the height, h, of the cylinder.
r
A radius of a base is also called a radius, r, of the cylinder.
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A cylinder is like a prism except that its bases are circles instead of polygons.
A cylinder is like a prism except that its bases are circles instead of polygons.
These are oblique cylinders.
Henceforth the word "cylinder" will always refer to a right cylinder.
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11.2 Notes.notebook
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Recall in a prism,
L.A. = ph
V = Bh
Thus....
A cylinder is like a prism except that its bases are circles instead of polygons.
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Theorem:
The lateral area of a cylinder equals the circumference of a base times the height of the cylinder.
L.A. = 2πrh
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11.2 Notes.notebook
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Theorem:
The volume of a cylinder equals the area of a base times the height of the cylinder.
V = πr2h
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11.2 Notes.notebook
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A cylinder has radius 5 cm and height 4 cm. Find the lateral area and the total area of the cylinder.
4 cm
5 cm
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11.2 Notes.notebook
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A cylinder has radius 5 cm and height 4 cm. Find the lateral area and the total area of the cylinder.
4 cm
5 cm
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11.2 Notes.notebook
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The radius of the base of a cylinder is 4 in. and its height is 6 in. What is the surface area of the cylinder in terms of π?
80 π in2
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A cylinder has a height of 9 cm and a radius of 10 cm. What is the surface area of the cylinder in terms of π?
380 π cm2
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11.2 Notes.notebook
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You are using the cylindrical stencil roller below to paint patterns on your floor. What area does the roller cover in one full turn?
47.1 in2
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11.2 Notes.notebook
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A smaller stencil roller has a height of 1.5 in. and the same diameter as the roller in the previous question. What area does the smaller roller cover in one turn? Round your answer to nearest tenth.
11.8 in.2
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What is the ratio of the smaller roller's height to the larger roller's height? What is the ratio of the areas the rollers can cover in one turn (smaller to larger)?
¼, ¼
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11.2 Notes.notebook
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The radius of the base of a cylinder is 6 cm its height is 15 cm. What is the surface area of the cylinder in terms of π.
252 π cm2
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A soup can is 4.5 in. high and has a diameter of 3 in. How much paper is needed to make a label that will completely cover the sides of the can without overlap?
about 42.4 in2
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What is the surface area of the cylinder?
48π cm2 or about 150.8 cm2
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11.2 Notes.notebook
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What is the surface area of the cylinder?
170π m2 or about 534.1 m2
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