Download Geometry Honors Section 7.1 Surface Area and Volume of

Geometry Section 12.2
Surface Area and Volume of Boxes
The *surface area of a 3dimensional object is the sum of
the areas of all of its exposed
surfaces.
The *volume of a 3-dimensional
object is the number of cubic units
needed to completely fill the
object.
NOTE:
If a unit of measure is given in the
problem, you must include the
appropriate unit on your answer.
The surface area S, and volume V,
of a box with length l, width w and
height h are
S = 2lw  2lh  2wh
V = l  w h
A cube is a special type of box
where the length, width and height
are all equal.
The surface area S, and volume V,
of a cube with edge e are
S=
6e
V=e
3
2
Example 1: Find the surface area and
volume of the two cereal boxes.
Sbox1  2  8  3  2  8  7  2  3  7  202 in
VBox1  8  3  7  168 in
2
3
S Box 2  2  2  8  2  2 10  2  8 10  232 in 2
VBox 2  2  8 10  160 in
3
Example 2: Find the height of a box
with a length of 2”, a width of 5” and a
surface area of 104 in2?
S  2lw  2lh  2 wh
104  2(2)(5)  2(2)h  2(5)h
104  20  4h  10h
84  14h
h6
Example 3: What is the length of an
edge of a cube if its volume is 405,224
mm3?
V e
3
405,224  e
3
e  3 405224
e  74