Am I wrong or is the textbook wrong?

I was helping someone I know out with a Maths question, but it seemed as if the textbook gave a different answer to the question than to the one we both got. Here is the question and all my working:

A rectangular prism has a square base $x$m and volume $8m^3$.

(i) Find an expression, in terms of x, for the height of the prism.

$8 = width x length x height [br][br]8 = x X x X h[br]8= x^2 X h[br]H = \frac{8}{x^2}[br][br]$

(ii) Hence, find the surface area of the prism.

The area of the prism's cross section is going to be: $h X x$, which means that it is $\frac{8}{x}$

The area of the base of the prism is: $x X x = x^2$

The prism's other face is also equal to $h X x$, so its area is $\frac{8}{x}$ too.

Which means that the total surface area of the prism is going to be all of those added together and multiplied by 2, hence the surface area is:

$\frac{16}{x} + \frac{16}{x} + 2x^2 = 2x^2 + \frac{32}{x}$. However the textbook says that the answer is $x^2 + \frac{32}{x}$

So have I done something wrong or is the textbook wrong?

*Sorry for the incorrect use of the = sign; I didn't know how to get the identical sign with LaTex.


Posted from TSR Mobile

I was helping someone I know out with a Maths question, but it seemed as if the textbook gave a different answer to the question than to the one we both got. Here is the question and all my working:

A rectangular prism has a square base $x$m and volume $8m^3$.

(i) Find an expression, in terms of x, for the height of the prism.

$8 = width x length x height [br][br]8 = x X x X h[br]8= x^2 X h[br]H = \frac{8}{x^2}[br][br]$

(ii) Hence, find the surface area of the prism.

The area of the prism's cross section is going to be: $h X x$, which means that it is $\frac{8}{x}$

The area of the base of the prism is: $x X x = x^2$

The prism's other face is also equal to $h X x$, so its area is $\frac{8}{x}$ too.

Which means that the total surface area of the prism is going to be all of those added together and multiplied by 2, hence the surface area is:

$\frac{16}{x} + \frac{16}{x} + 2x^2 = 2x^2 + \frac{32}{x}$. However the textbook says that the answer is $x^2 + \frac{32}{x}$

So have I done something wrong or is the textbook wrong?

*Sorry for the incorrect use of the = sign; I didn't know how to get the identical sign with LaTex.


Posted from TSR Mobile

use * or \times($\times$) to denote the multiplication operation. Equivalent is \equiv"$\equiv$".

Double check the question - if this is a solid prism then you are, of course, correct

The question says that it is an "open rectangular bank"

Then it does not have a "top" hence the missing $x^2$

Did it ask for the external surface area