can a sphere and a cube have simultaneously the same volume and area?

No my approach was similar to yours only I had a page of Latex which I lost.

Without doing any maths it appears obvious that it will not be possible.

I'm sure that Alan will come up with a much more intuitive logic as to why this cannot be.

I do not intend to redo mine.

Try this. Here is the ratio of a side on a cube to a sphere of equal volumes radius. http://www.wikihow.com/Determine-a-Cube-and-Sphere-of-Equal-Volume

A ratio of 1.6199. So for the the areas of each (found here in a formula) you can find what each value is for surface area and answer this question. http://math2.org/math/geometry/areasvols.htm 

Find a value for a, in a cube and value for r in a sphere (surface area formula), which fits the ratio and calculate the area. :D good luck. 

Hint, 

I just proved that this was impossible but the whole lot got delted on me.

I hate it when that happens!   

Mmmm.....this is an interesting question.......I don't really know!!!...let's see what happens.....

V_s = V_c   ????

Let's find the length of the side of the cube that  will make the volumes equal.....

(4/3)*pi*r³ = s³       take the cube root of both sides.......

r*[(4/3)*pi]^1/3  = s

So this is the length of the side of the cube that makes the volumes equal.

Now let's solve for the length of the side of the cube that makes the areas equal.....

A_s = A_c      ????

4*pi*r²  =  6s²      divide by 6 on both sides

(2/3)*pi*r² = s²       take the square root of both sides

r*[(2/3)*pi]^1/2  = s

And that's the length of the side of the cube that makes the areas equal.

But...it appears that we have a contradiction here.......the length of side of the cube that makes the volumes equal isn't the same as the length of the side of the cube that makes the areas equal. And since our cube isn't a "flexible" one, it seems that the answer to the question is........no.....

Anybody else have a different approach???.......there might be a more common sense reasoning....or perhaps I could be incorrect!!

"Anybody else have a different approach???.......there might be a more common sense reasoning....or perhaps I could be incorrect!!" CPhill. 

Same approach but different tact.

Note: I got in there with the right answer first. 

Stu I expect your answer is the better intuitive approach but you have not shown where 1.619 came from.

So your 'proof' is only the germ of an idea.

Well done, Stu.......I will give points to you and Melody......it appears that we all believe that it's impossible....however.....a consensus of opinion was once the justification for believing that the Earth was flat, too!!....

LOL!!!!!

Yes, that is exactly right Chris.

You can never assume in mathematics that something is so unless you can prove it!

You can have 3 points too Chris - yours is the best answer so far although with a little work I think Stu's answer would be better. 

Melody, I did show where the ratio came from on the link provided. Then the information to solve it. I think that it was a suitable answer for op to solve his own question which proves as a better answer since he'd learn more. :)

No Stu, you are doing uni maths.  You should be able to do the maths to show that number and not just copy it from another site.

Yes, but pushing the posters in the forum to self learning how to solve the information they need to calculate something is best, unless specifically asked otherwise which op didn't. Also since it's an anon poster I would rather take the push them in the right dirrection and simplest approach and if they repost/question then go more in depth. Although I didnt know the answer imidietly i could do it now. If they asked what is r means or is a ratio i'd tell them. If they asked where does the ratio value come from it's also there for them to see. The answer was enough, making the assumption only that they only want to know the fact about this question then there is proof how to resolve it which gives the answer just not the value or yes or no, 4 or 6.