Any maths wizards on here please? Updated

securityguy

claire21 wrote: »

Ok I'm back with the full question, sorry about yesterday, I thought you maybe just use an equation.

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?

Of course, the question's still incomplete: is the pyramid solid (ie, the volumes have to be the same) or made of sheets of wood (ie, the surface areas have to be the same)?

claire21

jack_pott wrote: »

Why is solving such a simple problem being a maths wizard? Little wonder we're so short of scientists and engineers.

I used wizard as an affectionate term, to you it may be simple, but then again there's lots of stuff I find simple that perhaps you don't.
It's nice to be nice.

MrsDrink

egoode wrote: »

He should work out the volume of the pyramid with the 230m length and width and height of 147m. Once he has the volume of that the volume will be the same for the base with 290m he just needs to change the formula to work out the height instead of volume.

Depends what the question means by "materials". Does it mean a solid pyramid or a skeleton, say made out of doweling?
Edit just read securityguy's comment about surface areas too.

So a filled 3D solid.
An empty 3D solid.
Or a skeleton 3D solid...

Actually would it matter? My head hurts. Been so long since I did proper maths. (I love Dara O Briains school of hard maths.

[Deleted User]

MrsDrink wrote: »

Depends what the question means by "materials". Does it mean a solid pyramid or a skeleton, say made out of doweling?
Edit just read securityguy's comment about surface areas too.

So a filled 3D solid.
An empty 3D solid.
Or a skeleton 3D solid...

Actually would it matter? My head hurts. Been so long since I did proper maths. (I love Dara O Briains school of hard maths.

There's a simple principle at work in exam questions: if you aren't given information, you don't need it. The only calculation you can make with the available information and assuming there's a finite amount of material is a constant volume calculation.

MrsDrink

jack_pott wrote: »

There's a simple principle at work in exam questions: if you aren't given information, you don't need it. The only calculation you can make with the available information and assuming there's a finite amount of material is a constant volume calculation.

Nope. It's a square based pyramid. Using Pythagoras you'd find the diagonal across the base. Half this. Then repeat Pythagoras using this half diagonal and the height to find out the length of the diagonal edges. Multiply by 4. Multiply base length by 4. Add together and you'd know how long a piece of doweling you'd need.
You can then work out how much would be left when you make a base of the new length. Divide the left over by 4 to find out the new length of the diagonal edges. Find the length of half the base diagonal as above. Then using this and the new diagonal edge you can then find out the height using Pythagoras.



Edit to say... Although the above is true. It doesn't work in the case of the above measurements. Because there isn't enough length to make a second square based pyramid of base length 290m


The original skeleton would be made using 1796.89m. Subtract 4 lots of 290 would only leave 636.894m for the new diagonals. Or 159.22m per diagonal edge.!
The length of !half the diagonal across the base is 205.06m so the diagonal edges wouldn't even reach the centre let alone stand up.

[Deleted User]

claire21 wrote: »

I used wizard as an affectionate term, to you it may be simple, but then again there's lots of stuff I find simple that perhaps you don't.
It's nice to be nice.

Quite, but we live in a society that regards it as normal to leave school unable to do basic maths, and that's not good for the economy. So long as those who can do the maths they were taught at school remain in a minority it's likely they'll continue to get labelled as weird geeks and nerds etc., and there'll be a consequential shortage of kids who aspire to be scientists and engineers rather than pop idols and celebs.

[Deleted User]

MrsDrink wrote: »

Nope. It's a square based pyramid. Using Pythagoras you'd find the diagonal across the base. Half this. Then repeat Pythagoras using this half diagonal and the height to find out the length of the diagonal edges. Multiply by 4. Multiply base length by 4. Add together and you'd know how long a piece of doweling you'd need.
You can then work out how much would be left when you make a base of the new length. Divide the left over by 4 to find out the new length of the diagonal edges. Find the length of half the base diagonal as above. Then using this and the new diagonal edge you can then find out the height using Pythagoras.



Edit to say... Although the above is true. It doesn't work in the case of the above measurements. Because there isn't enough length to make a second square based pyramid of base length 290m


The original skeleton would be made using 1796.89m. Subtract 4 lots of 290 would only leave 636.894m for the new diagonals. Or 159.22m per diagonal edge.!
The length of !half the diagonal across the base is 205.06m so the diagonal edges wouldn't even reach the centre let alone stand up.

You've already edited your post to refute your original argument, but that said, you didn't read my last post carefully either. I said "assuming a finite amount of material", your calculation only works assuming an infinitely thin dowel, in which case the quantity of material would be zero.

If you want to be pedantic, nobody has answered the question yet either, the volume of a pyramid has only been stated as V= LWH/3, but not calculated.

NY1986

jack_pott wrote: »

Quite, but we live in a society that regards it as normal to leave school unable to do basic maths, and that's not good for the economy. So long as those who can do the maths they were taught at school remain in a minority it's likely they'll continue to get labelled as weird geeks and nerds etc., and there'll be a consequential shortage of kids who aspire to be scientists and engineers rather than pop idols and celebs.

It's unbelievable and saddening the number of colleagues that can't do basic maths. Because I am in the process of doing a maths degree (through the OU) most people come to me to check their calculations.

One of the problems that this country will face because of the lack of people who are good at maths is teachers that are passionate about maths.

My high schools maths teacher was amazing and passionate about helping her students and is the reason why I am doing a maths degree.

ViolaLass

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.

bsms1147

"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.