Any maths wizards on here please? Updated

theoretica

bsms1147 wrote: »

If i was to build a pyramid out of bricks for example, and then build another pyramid twice the width also out of bricks, the second pyramid would be twice the height of the first.

Only if you were building to the material limits of the bricks. Your second pyramid of bricks could have a base of 290 and whatever height you fancied, below a certain quite tall height. I think keeping the same volume makes it a less badly worded question.

Though it probaby doesn't really matter - it is maths practice either way, which is the main point of this, rather than some random person on the internet getting the right answer.

ajwolf

bsms1147 wrote: »

"A squared based pyramid has base sides of 230 meters and a height of 147 meters. Using the same material, what would the height be if you have base sides of 290 meters?"

People are making this too complicated.

Nowhere does it say the volume is the same. Though the question is potentially ambiguous (bolded), it almost certainly refers to using the same material (that is, of the same intrinsic property as the first pyramid) rather than the same amount of material (volume if 3D, surface area if flat planes, length if a skeleton). It's a ratio question dealing with 3D scaling.

Ratio of new height to old height = ratio of new width to old width
Ratio of new height to old height = 290/230
Ratio of new height to old height = 1.26
New height = 1.26 x old height
New height = 1.26 x 147
New height = 185.3m

Just to add my agreement to the above and to add the following. In order for the shape to remain a similar square based pyramid you must increase (or decrease as questions can be asked that way around) all dimensions by the same factor. In this case the factor would be 1.26 (called Scale Factor).


The question wants you to build a similar shape. The new shape will be bigger than the original but the angles within the shape must remain the same, i.e. the incline from the corners of the base should be the same, not a shallower or steeper rise.


If you didn't use the same scale factor for each dimension the shape would start to look different from the original. If I took the same original shape and multiplied the base sides by 3 and the height only be 2 the angles at the four bottom corners would change resulting in a shallower incline up to the top point.


Hope this helps and sorry to anyone I bored with my maths.

ViolaLass

bsms1147 wrote: »

"A squared based pyramid has base sides of 230 meters and a height of 147 meters. Using the same material, what would the height be if you have base sides of 290 meters?"

People are making this too complicated.

I'm afraid you're the one overcomplicating this. What the OP hasn't said is that this is from a prep about volumes of square-based pyramids (I know because I've set it) so yes, it is about volume. By 'the same material'. they mean literally 'if we dismantled pyramid 1 and built pyramid 2'.

getmore4less

bsms1147 wrote: »

"A squared based pyramid has base sides of 230 meters and a height of 147 meters. Using the same material, what would the height be if you have base sides of 290 meters?"

People are making this too complicated.

Nowhere does it say the volume is the same. Though the question is potentially ambiguous (bolded), it almost certainly refers to using the same material (that is, of the same intrinsic property as the first pyramid) rather than the same amount of material (volume if 3D, surface area if flat planes, length if a skeleton). It's a ratio question dealing with 3D scaling.

Ratio of new height to old height = ratio of new width to old width
Ratio of new height to old height = 290/230
Ratio of new height to old height = 1.26
New height = 1.26 x old height
New height = 1.26 x 147
New height = 185.3m

[i.e. H2=H1x(W2/W1)]

If i was to build a pyramid out of bricks for example, and then build another pyramid twice the width also out of bricks, the second pyramid would be twice the height of the first.

Seriously?

If this is the standard of questions being set no wonder the kids of today don't have a clue.

Good specifications are the foundation of getting things right if kids are taught to second guess that is what they will do and get it wrong a lot of the time when it comes to new(to them) things.

For basic geometry why are the questions dressed up like this?

[Deleted User]

bsms1147 wrote: »

"A squared based pyramid has base sides of 230 meters and a height of 147 meters. Using the same material, what would the height be if you have base sides of 290 meters?"

People are making this too complicated.

Nowhere does it say the volume is the same. Though the question is potentially ambiguous (bolded), it almost certainly refers to using the same material (that is, of the same intrinsic property as the first pyramid) rather than the same amount of material (volume if 3D, surface area if flat planes, length if a skeleton). It's a ratio question dealing with 3D scaling.

It's just perverse interpreting "using the same material" as meaning the same shape. If we were talking about two pyramids of the same shape but different sizes, then the reference to "material" would be irrelevant, and a simple task would become utterly trivial.

Assuming that you're expected to look up (or remember) the formula for a pyramid volume rather than derive it, then the remainder of the puzzle is only primary school arithmetic as it is.

bsms1147

ViolaLass wrote: »

I'm afraid you're the one overcomplicating this. What the OP hasn't said is that this is from a prep about volumes of square-based pyramids (I know because I've set it) so yes, it is about volume. By 'the same material'. they mean literally 'if we dismantled pyramid 1 and built pyramid 2'.

That may be true, and I have no reason to doubt you.

However, the question worded as it stands has (at least) four very legitimate, very different, and each of them very correct answers.

[Deleted User]

ViolaLass wrote: »

I'm afraid you're the one overcomplicating this.

Aren't they just! I think the game here is to think up as many different ways of being obtuse as possible, but there are no marks in an exam for being a clever !!!!!!.

ViolaLass

bsms1147 wrote: »

That may be true, and I have no reason to doubt you.

However, the question worded as it stands has (at least) four very legitimate, very different, and each of them very correct answers.

I don't disagree but context is vital and the context here is that it's in a prep that is all about volume. That's probably why they've been a bit lax about the wording of the question. An exam question would be a lot more careful.

claire21

ViolaLass wrote: »

OP, out of curiosity, what year is your child in and what did they find tricky about this question? It's one that I've used with students too so it would be interesting to know.

He's 14 in year 10, he knows the formula for volumes of a pyramid, he "came"to the conclusion that the first sentence gave him a clue about how to work out the answer, but "first" he went trying to change the volume equation to see if that would work, he tried to find the slant angle etc. so actually studying the question was only after he tried to work out what he had been taught eg you are given 2 set measurements and work from there (looking at his notes) it was a set question on mymaths not a question set by his teacher. Hope that helps.

Edit I didn't really understand what the first line ment by saying "same material" but knowing it's only for a 14 year presumed it's the most basic of answer, no trick question.

Edit yet again : without logging back in to mymaths I believe the question was in volume section as it was the 3rd question on the computer page and the other 2 were about volume. Sorry I didn't say that in my post, sorry I didn't post the full question first of all as I thought that there was a much simpler answer that maybe we had overlooked.

Thanks for all that helped.

bsms1147

jack_pott wrote: »

Aren't they just! I think the game here is to think up as many different ways of being obtuse as possible, but there are no marks in an exam for being a clever !!!!!!.

Or just to think of as many solutions to a problem as possible.

No, of course you won't get marks for being a clever !!!!!! in exams, but as ViolaLass says, exam questions are tightened to the point where (usually) there isn't the scope for being one. That's not to say it isn't fun or interesting to have some lateral thinking on a wednesday evening. If only everyone was as enthusiastic about thinking outside the pyramid.

I loved maths back at school, still do now. I enjoy(ed) being a clever !!!!!! too.