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 cm^{3}

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 = 30x^{2}

^{
}

30x^{2} = 480

x^{2} = 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.

2x^{2} = 2(4)^{2} = 32 cm^{2}

^{
}

The four sides are rectangles with dimensions of width 4 cm and

height 30 cm for a total

area of

4(4)(30) = 480 cm^{2}

^{
}

32 cm^{2 }+ 480 cm^{2} = 512 cm^{2}