Any maths wizards on here please? Updated

JIL

Its a trigonometry question. The answer needs to be calculated using a formula with diagrams and a scientific calculator.
Its not basic to me.http://www.bbc.co.uk/schools/gcsebitesize/maths/geometry/furthertrigonometryhirev5.shtml

[Deleted User]

JIL wrote: »

Its a trigonometry question. The answer needs to be calculated using a formula with diagrams and a scientific calculator.
Its not basic to me.http://www.bbc.co.uk/schools/gcsebitesize/maths/geometry/furthertrigonometryhirev5.shtml

Good grief! The problem has already been solved for you in post 20 above, and again in post 47, there's no trigonometry involved. Even if you derive the volume of a pyramid from scratch there's still no trigonometry required:

Volume of a pyramid Dimensions L,W,H.

Length of the sides of a horizontal section at height z:

x = W(1-z/H)

y = L(1-z/H)

Area of the section:

a = xy = LW(1-z/H)^2

a = LW(1-2z/H+(z/H)^2)

Volume:

V = Integral (a) dz from 0 to H

= Integral (LW(1-2z/H+(z/H)^2))

= LW. Integral (1-2z/H+(z/H)^2)

= LW[z-z^2/H+z^3/(3H^2] from 0 to H

= LW[H-H^2/H+H^3/(3H^2)]

V = LWH/3


(This is not difficult maths. When I started work in the mid seventies other lads who had done traditional rather than SMP maths had already been doing this calculus at school!)

JIL

jack_pott wrote: »

Good grief! The problem has already been solved for you in post 20 above, and again in post 47, there's no trigonometry involved. Even if you derive the volume of a pyramid from scratch there's still no trigonometry required:

Volume of a pyramid Dimensions L,W,H.

Length of the sides of a horizontal section at height z:

x = W(1-z/H)

y = L(1-z/H)

Area of the section:

a = xy = LW(1-z/H)^2

a = LW(1-2z/H+(z/H)^2)

Volume:

V = Integral (a) dz from 0 to H

= Integral (LW(1-2z/H+(z/H)^2))

= LW. Integral (1-2z/H+(z/H)^2)

= LW[z-z^2/H+z^3/(3H^2] from 0 to H

= LW[H-H^2/H+H^3/(3H^2)]

V = LWH/3


(This is not difficult maths. When I started work in the mid seventies other lads who had done traditional rather than SMP maths had already been doing this calculus at school!)

I'm so sorry I asked someone who has a PhD in maths and physics and teaches maths to degree students. But then what would he know?

bsms1147

JIL wrote: »

I'm so sorry I asked someone who has a PhD in maths and physics and teaches maths to degree students. But then what would he know?

Clearly the person you asked knows their stuff, or they wouldn't hold the position they do. I imagine you asked them the wrong question though.

MrsDrink

I love Maths!!

securityguy

jack_pott wrote: »

When I was at school I did a modern maths syllabus called SMP instead of traditional maths. When I left, my employer wanted to know which I'd done, and when I told him he said "Oh, you'll struggle with the maths, then.". He was right, I had to work hard to keep up with those who had done traditional maths.

I've just Googled SMP, and it's still on the go according to Wikipedia! There's no wonder we're turning out kids who can't do maths if they're still teaching a syllabus that employers realised was useless as long as 40 years ago.

Define "employer". SMP, and its slightly more avant garde (and now dead) cousin MME, contains all the maths you need to work in computing (sets, some simple discrete maths, some number theory although it wasn't called that). If you're working in crypto or anything even vaguely related to it then the slightly dumbed down group and field theory that was in MME is useful. If you're working in computer games or graphics then some matrix work and some linear algebra is useful. If you're doing sales forecasting or materials planning linear programming is useful. More basically, how people can write computer programs, even simply expressions in Excel, without knowing some basic Boolean algebra is beyond me (hell, I had to explain to a computer science undergraduate recently that not (a and b) is equal to (not a or not b)). Writing computing programs and using spreadsheets: I gather it's done by quite a few people these days.

Calculus is much less useful than its exponents (ho ho) make out. The reason it was the sine qua non of engineering maths in the 1970s was that, before the routine use of computing, it made sense to fit a model to the data and then use calculus to derive things from that model. Today, it makes much more sense to keep the precision in the model, rather than fit a polynomial/trigonometric/whatever function to it. 1970s, throwing away precision in the curve fitting and then using calculus was the only game in town, today numerical methods are much more useful. Far more people do engineering with MATLAB, which is numerical, than do it with Mathematica, which is symbolic. Calculus is all present and correct, and much better taught than in my day, in the Additional maths FSMQ and in the initial C1 and C2 modules of A Level; however it's imply not as necessary as it was at the earlier stages, because numerical methods are more sensible. It might have been using for jobbing engineers in the 1970s. Now they use MATLAB. Times change. Logarithms are now taught properly in C1 rather than as a black box method to do multiplication in primary school, because we don't need them as a black box any more. So calculus, which was shockingly taught in the past, is now taught properly at an appropriate stage because it's not needed as a black box.

I've got a rag-bag of undergraduate-level maths, and I've worked in several engineering fields as well as computing. I can count on the fingers on one hand the occasions in the last twenty years I've used differential calculus, and I wouldn't have to take more than one sock off to count the number of times I've used integral calculus (for example, most recently I used it to check some calculations about compound interest on a monthly savings account, which is the obligatory money saving reference). I've used the matrix manipulation I did at O Level probably every few months, particularly the ability to invert n x n matrices as a way to solve systems of equations (and as maths conservatives love Khan academy, here's him doing the same thing).

If I had to choose between my children spending more time on calculus and spending time on some discrete maths, the discrete maths wins any time. And I've employed people.

ViolaLass

JIL wrote: »

I'm so sorry I asked someone who has a PhD in maths and physics and teaches maths to degree students. But then what would he know?

Well, apparently, he knows that questions with this kind of information could have involved trigonometry in the answer. It's not his fault, however, that you didn't give him all the information.

Not sure what relevance the PhD in maths has - this was only a GCSE question!

claire21

bsms1147 wrote: »

Algebraically...

H1 = 147
L1 = 230
W1 = 230
H2 = ?
L2 = 290
W2 = 290

V2 = V1

V1 = (H1 x L1 x W1)/3
V2 = (H2 x L2 x W2)/3

(H2 x L2 x W2)/3 = (H1 x L1 x W1)/3
H2 x L2 x W2 = H1 x L1 x W1
H2 = (H1 x L1 x W1)/(L2 x W2)
H2 = (147 x 230 x 230)/(290 x 290)
H2 = 7776300/84100
H2 = 92.46m

Thanks this is exactly what my son needed, this is how he is taught to work things out, He completely understands this method and thinks it was just the way the question was worded that he couldn't understand how to apply this method to it.

JIL

ViolaLass wrote: »

Well, apparently, he knows that questions with this kind of information could have involved trigonometry in the answer. It's not his fault, however, that you didn't give him all the information.

Not sure what relevance the PhD in maths has - this was only a GCSE question!

I suppose I answered with the mention of the PhD due to the response of "good grief" and being told there was no trigonometry involved.
I did ask the correct question. Maybe the fact the person I asked did not equate it to a GCSE question, given the fact they teach at a higher level, actually drawing me a diagram to show how it could be calculated.
Anyway I am glad the Op has an answer. And I will leave it at that.

theoretica

jack_pott wrote: »

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.

I am surprised no-one has pointed out yet that you don't need the formula for volume, but could work out this question (if properly worded!) for any shape.

Volume is proportional to Length x Depth x Height. If you increase length and want to keep volume constant you need to reduce height by the same proportion. Works for pyramids or statues of elephants, though the elephant would come out looking very odd.

Here you are increasing both length and depth so need to reduce the height twice - ie dividing by (290/230) squared.