Am I wrong or is the textbook wrong? Watch

crashMATHS
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#1
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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 xm and volume 8m^3.

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

8 = width x length x height 



8 = x X x X h

8= x^2 X h

H = \frac{8}{x^2}

(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.


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TenOfThem
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(Original post by kingaaran)
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 xm and volume 8m^3.

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

8 = width x length x height 



8 = x X x X h

8= x^2 X h

H = \frac{8}{x^2}

(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.


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Double check the question - if this is a solid prism then you are, of course, correct
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Kvothe the Arcane
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(Original post by kingaaran)
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 xm and volume 8m^3.

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

8 = width x length x height 



8 = x X x X h

8= x^2 X h

H = \frac{8}{x^2}

(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.


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use * or \times(\times) to denote the multiplication operation. Equivalent is \equiv"\equiv".
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crashMATHS
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(Original post by keromedic)
use * or \times(\times) to denote the multiplication operation. Equivalent is \equiv"\equiv".
Okay, thank you very much!


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crashMATHS
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(Original post by TenOfThem)
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"
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TenOfThem
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(Original post by kingaaran)
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
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crashMATHS
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(Original post by TenOfThem)
Then it does not have a "top" hence the missing x^2

Did it ask for the external surface area
Oh, I understand now! (facepalm) No, it just said work out the surface area. Thank you


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