We will work with right prisms, in which the slant
height is the same as the height. In order to solve problems which require application of the
volume and
surface area for prisms, it is necessary to
- V = area of base x height
- SA = sum of both bases and the lateral area
- regular polygon: base area =
- regular hexagon: base area =
A typical problem involving the
volume or
surface area of a prism gives us one or more of the volume, lateral area,
area of a base,
height and/or
radius of the prism. We will be required to calculate some of these quantities given information about the others.
To get started, we sketch a diagram and label all of the given information to determine the appropriate formula(s) we will be able to use.
Since we know the
volume is 480 cm
3, we will start with the formula for volume.
V = 480 cm3
V = lwh
The
length l and width
w are both the same in a
square base allowing us to use the
variable x for both
l and
w. Because
h is given as 30 cm we can write:
V = (x)(x)(30)
V = 30x2
30x2 = 480
x2 = 16
x = 4 cm
We will now use x = 4 cm and h = 30 cm to calculate the
area of all six rectangular sides of this prism. Remember that the 2 bases are equal as are the four sides making up the lateral area.
2x2 = 2(4)2 = 32 cm2
The four sides are rectangles with dimensions of width 4 cm and
height 30 cm for a total
area of
4(4)(30) = 480 cm2
32 cm2 + 480 cm2 = 512 cm2