Question

4 in.7 in18 in.4 in.The surface area of the rectangular prism issquare inches.The volume of the rectangular prism isy cubic inches.

Answer 1

We have been given a rectangular prism and we are required to find its surface area and volume.

We shall solve this question by first stating the formula of the parameter we want to find, then, we apply the respective formulas to find the values of these parameters.

Surface area:

The surface area is the sum total of all the areas of all the faces of the prism.

To solve this question, we need to note that there are 6 faces whose area we must calculate but out of the 6, there are two faces

each that are equal in area.

From the above figure, we have that:

FACE 1 = FACE 2

FACE 3 = FACE 4

FACE 5 = FACE 6.

Thus, once we find the area of FACE 1, we already have the area of FACE 2 and so on.

Also, since each face is a rectangle, the area of a rectangle is given by:

`\begin{gathered} A=l* b \\ l=\text{length} \\ b=\text{breadth or width} \end{gathered}`

Now, let us calculate the area of FACE 1, 3 and 5.

`\begin{gathered} \text{FACE 1:} \\ A_1=18*4=72in^2 \\ \text{FACE 3:} \\ A_3=4*7=28in^2 \\ \text{FACE 5:} \\ A_5=18*7=126in^2 \end{gathered}`

Now we just sum up all the areas and multiply them by two to account for FACES 2, 4 and 6

`\begin{gathered} A_S=2*(72+28+126) \\ \therefore A_S=452in^2\text{ } \end{gathered}`

Therefore, the Surface area of the rectangular prism is:

452 square inches

Volume:

The formula for the volume of a rectangular prism is given as:

`\begin{gathered} V=l* w* h \\ l=\text{length} \\ w=\text{width or breadth} \\ h=\text{height or depth} \end{gathered}`

The length, width, and height are shown in the figure below:

Thus, we can easily calculate our volume as shown below:

`\begin{gathered} V=7*18*4in^3 \\ \therefore V=504in^3 \end{gathered}`

Therefore, the Volume of the rectangular prism is:

V = 504 cubic inches

To recap, the final answers are:

Surface Area = 452 square inches

Volume = 504 cubic inches