1. ## Variation problem

So Im having a hard to remembering how to work this out. Here is the problem:

The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cumbical container 4cm on a side is 128 g, find the weight of the liquid in a cubical container 3cm on a side.

2. This is a simple ratio:

weight 128 x
volume 64 27

64x = (128)(27)
x = 54

Note that we cubed 4 and 3 because these are lengths of sides, and the weight varies directly as its VOLUME.

3. where did the 27 come from ?

nvm you cubed the 3.. thanks

4. 3 is the length of a side, so the volume is $3^3 = 27$.

The gravatational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 9 lb when the masses are 2 ft apart, what is the attraction when the masses are 6 ft apart?

6. In a direct variation problem (like the earlier one) you set quotients equal to each other. In an inverse variation problem (like this last one) you set products equal to each other.

(9)(4) = (x)(36)

So x = 1

Note that we squared 2 and 6.

7. Ok cool thanks man