# What is a surface area of a cube with the volume of $8cm^3$?

Right, a cube with a volume of $8cm^3 =(2 \times 2 \times 2)$, what is the surface area? I think it's $8cm$, but I'm not sure and how do you work it out? My tutor sys it's $24cm$ but how is it? I've searched on the internet and it says you should do $l \times h \times w$. Confused?

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You mean a cube with volume $8cm^3$? – Lost1 Apr 11 '13 at 12:28
yeah volume lol, sorry – user61406 Apr 11 '13 at 12:29
Hi, Honky! Since you've asked a few questions now, and received some nice answers, I thought I'd encourage you to accept and upvote helpful answers. You can accept only one answer per question, just click on the $\large \checkmark$ to the left of the answer you'd like to accept. (You get two reputation points for each answer you accept.) AND you can Upvote as many answers as you'd like. – amWhy Apr 13 '13 at 18:00
that helps, thanks – user61406 Apr 14 '13 at 10:28

I think what you mean is that you have a cube of $\textbf{volume}$ $\ 8\text{cm}^3$=2cm x 2cm x 2cm.

A cube has 6 faces of equal area.

Therefore, the total surface area of the cube is equal to 6 multiplied by the area of one of the faces.

The area of one of the faces is 4$\text{cm}^2$ = 2cm x 2cm.

Therefore the total area of the cube is 24$\text{cm}^2$ = 6 x 4$\text{cm}^2$.

One thing you must remember is your units of measurement, writing 8cm2 (2x2x2) really makes no sense, since you are equating an area with a single number without units.

The result of your internet search has returned the method for working out the volume of the cube (or in fact a cuboid).

Volume = Length x Width x Height $\ \$ (cm$^3$ = cm x cm x cm)

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Hint. A cube is composed of 6 same squares, each of area $2\times2\mathrm{cm}^2$.

Also I asume you mean it has volume of $8\mathrm{cm}^3$.

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yes! the volume is 8cm3 – user61406 Apr 11 '13 at 12:29

You're confused. If a cube is $2\text{cm}\times2\text{cm}\times2\text{cm},$ then it has a volume of $8\text{cm}^3$, not an area of $8\text{cm}^2$. Note that each of its faces is $2\text{cm}\times2\text{cm}$, so has an area of $4\text{cm}^2$. How many faces does a cube have?

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6, yeah it's 24, thanks – user61406 Apr 11 '13 at 12:30
The actual formula for the surface area of a box in general is $$2(lw+wh+lh),$$ if you're curious. – Cameron Buie Apr 11 '13 at 12:42