Surface Area of Rectangular Prisms
Example:
Jeff bought his
mom a box of
chocolates for
Mother’s Day
(aww). If the box
is rectangularprism-shaped with
a length of 5.4 cm,
a width of 2.8 cm,
and a height of 1.5
cm, how much gift
wrap will he need
to wrap it up?
http://greatmathsgames.co
m/maths/nets/rectangular_
prism/rectangular_prism_ne
t.gif
1.5
cm
SA = 2 l w + 2 l h + 2 w h
SA =2( 5.4 )( 2.8 )+ 2( 5.4 )( 1.5 )+ 2( 2.8 )( 1.5 )
SA = 30.24 + 16.2 + 8.4
SA = 54.84 ≈ 54.8 cm2 or 54.8 sq cm
Surface Area of Cylinders
3.1 ft
Example:
http://greatmathsgames.c
Jackie has an old,
om/maths/nets/cylinder/
cylinder_sm.gif
aluminum garbage
1.8 ft
can that she wants
to repaint. If the
garbage can is
SA= 2πrh
+ 2 πr2
cylinder-shaped,
with a diameter of S A = 2( π )( 0.9 )( 3.1 ) + 2( π )( 0.9 )( 0.9 )
1.8 ft and a height
of 3.1 ft, how
+
5.09
much paint will SA = 17.53
she need?
SA = 22.62 ≈ 22.6 ft2 or 22.6 sq ft
Volume of Rectangular Prisms
Example:
Bud has a cubeshaped
container that
he fills with
compost. If the V = l w h
container’s
length is 1.2 m
V =(1.2 )( 1.2 )( 1.2 )
long, how
much compost
will it take to V = 1.728 ≈ 1.7 m3 or 1.7 cubic meters
fill it up?
V
l w h
Example:
Wilma has a V = π r2 h
rain gauge that
is shaped like a
cylinder. It’s V =( π )( 0.2 )( 0.2 )( 1.9 )
1.9 yd tall and
has a radius of V = 0.238 ≈ 0.2 yd3
0.2 yd. What
or
is the capacity
0.2 cubic yards
of Wilma’s rain
gauge?
1.9 yd
Volume of Cylinders
0.2
yd
Changing Volume
Cleveland’s moving, so he’s buying boxes. There’s a small and a extra-large.
All dimensions (length, width, height) are 4 times longer on the extra-large box.
How much more will the extra-large box hold?
To find the change in volume, use this formula:
sf
4
3
64
scale factor
(
# of dimensions
changed
)
Since each dimension is 4 times bigger, the scale factor is 4.
And, since all 3 dimensions changed, the exponent is 3.
The extra-large box holds 64 times more than the small.
When he compares the
small to the medium , he
finds only the length is 4
times longer. How
much more will the
medium box hold?
4
1
4
The medium
box holds 4
times more
than the
small.
When he compares the
small to the large, he
finds the length and
width are 4 times longer.
How much more will
the large box hold?
4
2
16
The large box
holds 16 times
more than the
small.
Changing Surface Area
For Valentine’s Day, Neil bought Meg a little jewelry box, and a huge box of chocolates.
All dimensions of the huge box of chocolates are 5 times longer than the little jewelry box.
How much more wrapping paper will he need for the huge box of chocolates?
To find the change in surface area, use this formula:
sf
5
2
2
25
scale factor
2
We’ll only solve surface area
problems in which all
dimensions change by the
same factor. There’s no easy
formula when only 1 or 2
dimensions are changed.
Since each dimension is 5 times bigger, the scale factor is 5.
The huge box of chocolates needs 25 times more
wrapping paper.
All the dimensions of
large trunk are 3 times
longer than a small
trunk. How much more
stain is needed to cover
the large trunk?
The large
one needs
3
2
9
9 times
more
stain.
All the dimensions of
a big sugar cube are
100 times longer than
one grain of sugar.
How much more
surface does the big
one have?
The large
one has
100
2
10,000
10,000
times
more
surface.