# box volume/surface area

• Dec 1st 2010, 06:16 AM
Joker37
box volume/surface area
A box with a volume of $\displaystyle 400 cm^{3}$has the shape of a rectangular prism. It has a fixed height of $\displaystyle 25 cm$, a length of y cm and a width of x cm. If $\displaystyle A cm^{2}$ 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!
• Dec 1st 2010, 06:41 AM
VonNemo19
They want a formula for the Surface area that has nothing but x's in it.

Example:

Perimiter is $\displaystyle p=2x+2y$. If $\displaystyle y=2x+6$, then p expressed in terms of x is $\displaystyle p(x)=2x+2(2x+6)$.
• Dec 1st 2010, 06:44 AM
e^(i*pi)
Express A in terms of x means A = some function of x. In other words it doesn't want any $\displaystyle y$ in there

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

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

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

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

You can use eq1 to eliminate y in eq2
• Dec 1st 2010, 08:04 PM
Joker37
$\displaystyle V=xyz$

$\displaystyle V=400, z=25$

$\displaystyle xy=16, y=\frac{16}{x}$
$\displaystyle A= 2(xy+25y+25x) =32+50y+50x =32+50(\frac{16}{x}) +50x$
$\displaystyle A=32+\frac{800}{x}+50x$
• Dec 1st 2010, 08:23 PM
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?
• Dec 2nd 2010, 06:53 AM
e^(i*pi)
Quote:

Originally Posted by Joker37
$\displaystyle V=xyz$

$\displaystyle V=400, z=25$

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

Yes that's correct

Quote:

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 $\displaystyle V = A_Ch$ where $\displaystyle A_C$ 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:

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

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

$\displaystyle V_{cone} = \dfrac{1}{3}Ah$ 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