# Pure Maths differentiation, area and volume

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#1
A fish tank in the shape of a cuboid is to be made from 1600 cm^2 of glass.
The fish tank will have a square base of side length x cm, and no lid. No glass is wasted. The glass can be assumed to be very thin.
(a) Show that the volume, V cm , of the fish tank is given by V = 400x -x^3/4
(b) Given that x can vary, use differentiation to find the maximum or minimum value of V.
(c) Justify that the value of V you found in part b is a maximum.
0
3 years ago
#2
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2 years ago
#3
Basically, the length and width are both x therefore , surface area will equal to x^2 2xh 2xh which will be x^2 +4xh=1600 rearrange for h which will be h= 400/x - x/4 then you sub that into volume= x^2h and simplify it - for part a
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1 year ago
#4
The mark scheme is on this, I just had this on a test and it annoyed me. What kind of psycho has a vertical fish task! https://portal.hppc.co.uk/files/vaca...pper_maths.pdf
0
1 year ago
#5
(Original post by Hanson.p)
The mark scheme is on this, I just had this on a test and it annoyed me. What kind of psycho has a vertical fish task! https://portal.hppc.co.uk/files/vaca...pper_maths.pdf
Same! Came up on a test today and spent way too long on it
1
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