box volume/surface area

**Joker37** · December 1st 2010, 06:16 AM

A box with a volume of $400 cm^{3}$ has the shape of a rectangular prism. It has a fixed height of $25 cm$ , a length of y cm and a width of x cm. If $A cm^{2}$ is the total surface area:
a) Express A in terms of x.

I don't understand what it means when it says 'express A in terms of x'. Anyway if someone could provide detailed working out to this it will be appreciated!

**VonNemo19** · December 1st 2010, 06:41 AM

They want a formula for the Surface area that has nothing but x's in it.

Example:

Perimiter is $p=2x+2y$ . If $y=2x+6$ , then p expressed in terms of x is $p(x)=2x+2(2x+6)$ .

**e^(i*pi)** · December 1st 2010, 06:44 AM

Express A in terms of x means A = some function of x. In other words it doesn't want any $y$ in there

The volume of a cuboid (a rectangular prism is a cuboid) is $V = xyz$ . You are given $V = 400$ and $z = 25$

The surface area of a cuboid is $2(xy+yz+xz)$ (in other words the sum of the six faces)

From the expression for volume you get $16 = xy$ (eq1)

and from the expression for area: $A = 2(xy+25y+25x)$ (eq2)

You can use eq1 to eliminate y in eq2

**Joker37** · December 1st 2010, 08:04 PM

$ V=xyz $

$ V=400, z=25 $

$ xy=16, y=\frac{16}{x} $
$A= 2(xy+25y+25x) =32+50y+50x =32+50(\frac{16}{x}) +50x $
$ A=32+\frac{800}{x}+50x $

**Joker37** · December 1st 2010, 08:23 PM

Thanks for the help VonNemo19 and e^(i*pi)!

Incidentally, do you guys think that it's beneficial to memorise all these equations we use in geometry (i.e. the surface area of a cuboid, volume of a sphere, volume of cylinder etc)? Generally is it recommended that people memorise all of these equations?

**e^(i*pi)** · December 2nd 2010, 06:53 AM

Originally Posted by Joker37

$ V=xyz $

$ V=400, z=25 $

$ xy=16, y=\frac{16}{x} $
$A= 2(xy+25y+25x) =32+50y+50x =32+50(\frac{16}{x}) +50x $
$ A=32+\frac{800}{x}+50x $

Yes that's correct

Originally Posted by Joker37

Thanks for the help VonNemo19 and e^(i*pi)!

Incidentally, do you guys think that it's beneficial to memorise all these equations we use in geometry (i.e. the surface area of a cuboid, volume of a sphere, volume of cylinder etc)? Generally is it recommended that people memorise all of these equations?

I tend to think of them logically. For example the volume of a prism is $V = A_Ch$ where $A_C$ is cross sectional area and h the height. For a cylinder the cross section is a circle and for a cuboid it's a rectangle both of who's areas are easy to work out.

Surface area is a logical one for me, in this problem I imagined a rectangle which will have 3 pairs of faces (hence the 2 outside the brackets) and those faces are simply squares.

The only ones I tend to remember are:

$V_{sphere} = \dfrac{4}{3}\pi r^3$

$A_{sphere} = 4\pi r^2$

$V_{cone} = \dfrac{1}{3}Ah$ where A is the area of the base and h the perpendicular height from the apex.

edit: I should mention that in some exams you are given certainly formulae, make sure you know what these are so you don't have to remember them, just what they do

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