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.
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FSMQ Additional Maths help watch
- Thread Starter
Last edited by xxjessietxx; 17-04-2016 at 18:19.
- 17-04-2016 18:08
- 18-04-2016 14:10
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'
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
2h^2 = 50/3
h^2 = 25/3
h = square root of 25/3
Hope that helped! (: