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# Maths People Help Please!! :) watch

1. Question:

A cuboid has a square base of length x metres and height y metres.
(a) Express the volume in terms of x and y
(b) Show that the surface area of the cuboid is 2x^4+4xy

then...

the surface area of the cuboid is 24cm^2

(c)Show that V=6x-0.5x^3
(d)Show that the maximum volume of the box occurs when x=2 and find this maximum value.

2. For a) + b) draw the cuboid and name the vertices. That should help a lot. (+ the surface is 2*x^2, isn't it?)

For c) find y in terms of V and x. Substitute into equation of area. Solve to obtain V.

For d) differentiate and equate what you got to 0. Solve to obtain x.
3. Call me stupid, but I'm still quite confused?!
4. a) Draw the cuboid. Name the vertices (width, depth, height) in terms of x and y. The volume is width x depth x height.

b) Surface area is the area of all (six) small surfaces.

c) 24 = 2x^2+4xy

V = some equation in terms of x and y

Find y in terms V and x

Substitute the equation for y in place of y in the equation for the surface area. Solve to obtain V in terms of x.

d) Differentiate V with respect to x. Equate dV/dx = 0. Solve to obtain x. Find the maximum volume.
5. But I don't have the depth?

so I would have
V=ydx?
6. the base is SQUARE x by x and u have a height y...

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Updated: February 6, 2010
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