The Student Room Group

This discussion is now closed.

Check out other Related discussions

Maths People Help Please!! :)

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.

does it have anything to do with differentiation at all? please help guys! :eek3:
Reply 1
Avatar for goldsilvy
goldsilvy
15
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.
Reply 2
Avatar for s25s
s25s
OP
Call me stupid, but I'm still quite confused?!
Reply 3
Avatar for goldsilvy
goldsilvy
15
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.
Reply 4
Avatar for s25s
s25s
OP
But I don't have the depth?

so I would have
V=ydx?
Reply 5
Avatar for lee_91
lee_91
10
the base is SQUARE x by x and u have a height y...

Related discussions

Latest

Trending

Trending

Articles for you