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FSMQ Additional Maths help

Hi! I'm still trying the additional maths past paper and I have done the first two parts of this question but are unable to do the rest.

A pyramid has a square base, ABCD, with vertex E. E is directly above the centre of the base, O.
The lengths of the sides of the base are each 2x metres and the height is h metres.
The lengths of the sloping edges, AE, BE, CE and DE, are each 5 metres.

i) Show that 2x to the power of 2 = 25-h to the power of 2.
I have done this question

ii) Show that the volume of the pyramid, Vm to the power of 3 is given by
V= 50h-2h to the power of 3
divided by 3

I have already answered this question

iii) As h varies, find the value of h for which V has a stationary value.

(edited 8 years ago)

Reply 1

F3rnw3h

We know that 'V=50h-2h^3/3'

We also know that at a stationary point, the dv/dh is equal to 0
therefore, we have to differentiate 'V=50h-2h^3/3'

So...

dv/dh = 50h/3 - 2h^3/3

=50/3 - 6h^2/3
=50/3 - 2h^2

Because dv/dt = 0

50/3 - 2h^2 = 0

So

2h^2 = 50/3
h^2 = 25/3
h = square root of 25/3
h= 2.89

Hope that helped! (: