Surface area of Right Prisms and Cylinders
MA202 Sections 5 & 401
Chapter 12-4 Slides
Surface area of Right Prisms and Cylinders
SA = 2B + ph
MA202 Sections 5 & 401
Chapter 12-4 Slides
Example 12.19
We have a strangely shaped gift box. The long sides of the base
are 20cm, the shorter sides of the base are 5cm. The height of the
box is 10cm. Find the total Surface Area.
MA202 Sections 5 & 401
Chapter 12-4 Slides
Example 12.20
Given a small can of frozen orange juice that is 9 cm tall and has a
diameter of 5 cm. If the circular ends are metal, and the sides of
the can are cardboard: how much metal and how much cardboard
do we need to make a juice can?
MA202 Sections 5 & 401
Chapter 12-4 Slides
Surface area of Right Regular Pyramids
MA202 Sections 5 & 401
Chapter 12-4 Slides
Surface area of Right Regular Pyramids
1
SA = B + ps
2
MA202 Sections 5 & 401
Chapter 12-4 Slides
Example 12.21
A pyramid has a square base that is 10 cm on a side. The edges
that meet at the apex have length 13 cm. Find the slant height of
the pyramid and then calculate the total surface area of the
pyramid.
MA202 Sections 5 & 401
Chapter 12-4 Slides
Surface area of Right Circular Cones
SA = πr 2 + πrs
MA202 Sections 5 & 401
Chapter 12-4 Slides
Example 12.22
An ice cream cone has a diameter of 2 inches and a slant height of
6 inches. What is the lateral surface area of the cone?
MA202 Sections 5 & 401
Chapter 12-4 Slides
Volume of Right Prisms and Cylinders
V = Bh
MA202 Sections 5 & 401
Chapter 12-4 Slides
Example 12.23
Find the volume of the gift box and the juice can.
MA202 Sections 5 & 401
Chapter 12-4 Slides
Volume of General Prisms and Cylinders
V = Bh
MA202 Sections 5 & 401
Chapter 12-4 Slides
Volume of General Pyramids and Cones
1
V = Bh
3
MA202 Sections 5 & 401
Chapter 12-4 Slides
Example 12.24
The pyramid of Khafre is 145m high, and its square base is 215m
on each side. What is the volume of the pyramid?
http://www.egyptarchive.co.uk/html/khafre_01.html
MA202 Sections 5 & 401
Chapter 12-4 Slides
Volume of a Sphere
4
V = πr 3
3
MA202 Sections 5 & 401
Chapter 12-4 Slides
Example 12.25
An ice cream cone is 5 inches high and has an opening 3 inches in
diameter. If the cone is filled with ice cream and given a
hemispherical top, how much ice cream is there?
MA202 Sections 5 & 401
Chapter 12-4 Slides
Surface Area of a Sphere
SA = 4πr 2
MA202 Sections 5 & 401
Chapter 12-4 Slides
Example 12.26
The diameter of Jupiter is about 11 times larger than that of
Earth. How many times greater is the Surface Area of Jupiter? the
Volume of Jupiter?
MA202 Sections 5 & 401
Chapter 12-4 Slides
Example 12.26
The diameter of Jupiter is about 11 times larger than that of
Earth. How many times greater is the Surface Area of Jupiter? the
Volume of Jupiter?
SA of Jupiter
4πR 2
=
=
SA of Earth
4πr 2
MA202 Sections 5 & 401
2
R
= 112
r
Chapter 12-4 Slides
Example 12.26
The diameter of Jupiter is about 11 times larger than that of
Earth. How many times greater is the Surface Area of Jupiter? the
Volume of Jupiter?
2
R
= 112
r
3
4
3
V of Jupiter
R
3 πR
= 4 3 =
= 113
V of Earth
r
πr
3
SA of Jupiter
4πR 2
=
=
SA of Earth
4πr 2
MA202 Sections 5 & 401
Chapter 12-4 Slides
The Similarity Principle of Measurement
Theorem
Let Figures I and II be similar. Suppose that some length
dimension of Figure II is k times the corresponding dimension of
Figure I; that is k is the scale factor:
any length measurement (perimeter, diameter, height, slant
height, etc) of Figure II is k times that of the corresponding
measurement in Figure I.
any area measurement (surface area, area of base, etc) of
Figure II is k 2 times that of the corresponding measurement
in Figure I.
any volume measurement (volume, capacity, etc) of Figure II
is k 3 times that of the corresponding measurement in Figure I.
MA202 Sections 5 & 401
Chapter 12-4 Slides
Example 12.27
1
The size of television sets are measured by the length of the
diagonal of their screen. How many times larger is the screen
area of a 40” TV than a 20” TV?
2
A 2” by 4” by 8” rectangular brick of gold weighs 80 lbs.
What are the dimensions of a similarly shaped brick that
weighs 10 lbs?
MA202 Sections 5 & 401
Chapter 12-4 Slides
Example 12.27
1
The size of television sets are measured by the length of the
diagonal of their screen. How many times larger is the screen
area of a 40” TV than a 20” TV?
2
A 2” by 4” by 8” rectangular brick of gold weighs 80 lbs.
What are the dimensions of a similarly shaped brick that
weighs 10 lbs?
1
k = 40/20 = 2, so area increases by a factor of k 2 = 4.
MA202 Sections 5 & 401
Chapter 12-4 Slides
Example 12.27
1
The size of television sets are measured by the length of the
diagonal of their screen. How many times larger is the screen
area of a 40” TV than a 20” TV?
2
A 2” by 4” by 8” rectangular brick of gold weighs 80 lbs.
What are the dimensions of a similarly shaped brick that
weighs 10 lbs?
1
2
k = 40/20 = 2, so area increases by a factor of k 2 = 4.
Weight corresponds to volume, so the factor is
k 3 = 10/80 = 1/8. Thus k = 1/2. So a 10 lb brick would
have dimensions 1” by 2” by 4”.
MA202 Sections 5 & 401
Chapter 12-4 Slides
Class Discussion
To find SA of a hemisphere, be sure to add the area of the
base.
When responding to Samuel, remember that he is holding the
height constant.
MA202 Sections 5 & 401
Chapter 12-4 Slides
Homework
Homework 7 (due 4/6/10):
Section 12.3 # 2ac, 3, 4ab, 5, 6, 9, 32
Section 12.4 # 2b, 3c, 4d, 5d, 6ab, 19a, 23
MA202 Sections 5 & 401
Chapter 12-4 Slides