They want a formula for the Surface area that has nothing but x's in it.
Example:
Perimiter is . If , then p expressed in terms of x is .
A box with a volume of has the shape of a rectangular prism. It has a fixed height of , a length of y cm and a width of x cm. If 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!
Express A in terms of x means A = some function of x. In other words it doesn't want any in there
The volume of a cuboid (a rectangular prism is a cuboid) is . You are given and
The surface area of a cuboid is (in other words the sum of the six faces)
From the expression for volume you get (eq1)
and from the expression for area: (eq2)
You can use eq1 to eliminate y in eq2
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?
Yes that's correct
I tend to think of them logically. For example the volume of a prism is where 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:
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