Memory Aid
be able to work backwards to find the
radius or a length, use examples.
all the volumes and areas are on p 84 of
text book (hard cover)
Surface area: add up the area of all the sides
it is the total area
sphere: 4 (3.14) r2
Volume: prisms: area of the base x the height
use the formulas
cones and pyramids we take the area of the base x
height divide by 3)
sphere: v = 4(3.15)r3/3
Things you need to know
If the area of a square is ex. 625cm2
Find a side (s)
s2 = 625 cm2
s = 25cm
If the volume of a cube is 27m3
s3 = 27m3
s = 3m
1
Find the surface area of a sphere whose volume is 113040 cm3
Write the formulas down
v = 4(3.14)r3/3 = 113040
find r!!!!!!
cross multiply and isolate r.
r= 30cm
SA = 4 (3.14) r2
= 4 (3.14) (302)
= 11304 cm2
When an image is 5 times the size of an object
k=5
the area will be 5 x 5 times bigger
the volume will be 5 x 5 x 5 times bigger
ex. a sphere is twice as big as a sphere with r = 10cm
the new sphere will have an a surface rea 2 x 2 = 4 times
bigger
the volume will be 2x2x2 = 8 times bigger.
ex. a cube is one third the size of another
its sides will be 3 times smaller
its area will be 9 times smaller
its volume will be 27 times smaller
2
The volume of a rectangular prism is 162cm3
its surface area is 198 cm2
Another similar rectangular prism has a volume of
1296cm3
What is the area of the new rectangular prism?
k3 = 1296/162
=8
k=2
Area: 4 times bigger
198 x 4 = 792 cm2
For each of the following situations, find the unknown
measurement of the equivalent figures or solids
4
?
8
3
3
?
5
25
lxw
10
can/2
Pull hint
2 Equivalent solids
Pull
volume
4dm
4dm
height
slant height
find the height of the cone
What is the slant height ?
4
radius of the cylinder is the same as the
radius of the cone
3cm
?
r
r
v = area of base x h
v = area of base x h
3
Pull hint
Find the height if they have the same radius = 9 cm and they are equivalent
?
r
r
v = πr 2 x h
πr2 h
cancel out π
v=
=
4πr3
3
4πr3
3
r2h = 4r3
3
cancel out some of the r's
r2h = 4r3
3
h = 4r/3
So whatever the radius,
when a cylinder and sphere are equivalent
the height of an equivalent cylinder will be 4/3
times the radius.
Example: if the radius of both the sphere and the
base of the cylinder is 3cm,
then the height of the clineder is 4cm
5
Quiz:
1) Find the width to the nearest cm of the rectangle
that is equivalent to the circle
30 cm
r = 15cm
2) find the length of a side of the cube that is equivalent
to the prism.
2
36
3
3) what is the surface area of the cube?
If ever you are given a question with more than one
unknown, write out the formulas,
show that the 2 areas or volumes are equal
and cancel out the shared values
(r is common)
6
What is maximum volume of the cone...
What is maximum volume of the cone...
that can fit insides the cylinder
that can fit insides the cylinder whose volume is 3000cm3?
r
h
What is maximum volume of the cone...
that can fit insides the cylinder whose volume is 3000cm3?
r=r
area of the base = area of the base
h=h
r
volume of cylinder
area of base x h
h
area of the base x h is
equivalent for both
volume of the cone
area of the base x h
3
next page....
7
What is maximum volume of the cone...
that can fit insides the cylinder whose volume is 3000cm3?
(the answer will be in terms of the cylinder)
r=r
area of the base = area of the base
volume of cylinder
volume of the cone
h=h
area of the base x h
3
area of base x h
r
h
Volume of the cone = volume of the cylinder
3
vol = 3000cm3 = 1000cm3
3
A person is making cushions (pillows)
What is the volume of the largest cushion the person
can make using 2.2 m2 of fabric. He wants rectangular
shaped cushions.
one side = x
x2 = 2.2m2
x = 1.48m
volume = x3 =3.26m3
or 3.24 if you rounded off
in cm?
k = 100
3.26 x k3
3.26 x 1003
3263127.3cm3
picture a cm cubed, tiny
picture 3 m cubed... very large
8
scale factor: with similar figures
if the length is 5 times as big: k=5
multiply the area by 52 (25) if going from smaller to bigger.
If we know the bigger area divide by 25
Volume: k=5 mulitiply or divide by 53 = 125
converting units in the
metric system
there are 100 cm in a meter
lengths
m to cm is x 100 k= 100
areas
m2 to cm2 multiply by k2 = 10000
volumes
m3 to cm3 multiply by k3 = 1000000
If going from cm to m, then divide
km to cm k=
km to m
k=
dm to cm
k=
dm to m
k=
10 mm in a cm
100cm in a m
10cm in a dm
The prefix is in relation to 1m
km
dm
m
cm
mm
1000m
1m
0.1m
0.01m
0.001m
divide by 1000 divide by 100 divide by 10 equal multiply by 1000
9