Thread: proportions

ok so here we go....

for any cube, if the volume is V cubic inches and the surface area is A square inches, then V is directly proportional to which of the following

a. A

b. A^2

c. A^3

d. A^(2/3)

e. A^(3/2)


so in this problem am i to compare volume to surface area?

or say that volume is proportional to surface area?

V^3 = K*A^2

but in a cube and square the lengths are the same, right?

so I can say A^3 = K*A^2?

i dunno this setup seems wrong, but im not seeing where i am making the mistake...

k in this problem is the proportion constant.....

Yes, in a cube and a square which is a face of the same cube, the side length is the same. Use that side length, s, as the "connection". The volume is proportional to : . And the area is proportional to the area: . Eliminate s from those two equations to get a formula in only V and A.

(And what you give: does NOT say "volume is proportional to area", it says "volume cubed is proportional to area squared".)

ok so s = V^(1/3) and s = A^(1/2)...

ok so V^(1/3) = K*A^(1/2)

ok so V = k*A^(3/2). thanks!

Yes. You could also have reasoned that s= A^(1/2) so V= s^3= (A^(1/2))^3= A^(3/2). Notice that here k happens to be 1. It is, in fact, true for any object that the volume is proportional to the surface are to the 3/2 power. For a cube the constant of proportionality is 1.