Question

The weight of a synthetic ball varies directly with the cube of its radius. a ball with a radius of 2 inches weighs 1.60 pounds. find the weight of a ball of the same material with a​ 3-inch radius.

Answer 1

Quick answer: 5.4 pounds for a ball 3" in radius.
Remark
You are expected to do this by calling 4/3*pi = some constant k

Givens
r = 2 inches
r1 = 3 inches

Ratio
$\frac{W1}{W2} = \frac{k r^3}{k (r1)^3}$

Sub and solve 
Begin by cancelling out the ks.
$\frac{W1}{W2} = \frac{r^3}{(r1)^3}$

Next substitute for the 2 rs.
$\frac{W1}{W2} = \frac{2^3}{3^3}$

Now expand the 2 cubic amounts.
$\frac{W1}{W2} = \frac{8}{27}$

Conclusion Part One
The ratio of the two weights is 8/27

Part Two
Set up the ratio for 1.6 pounds to x
$\frac{8}{27} = \frac{1.6}{x}$

Cross multiply
8*x = 27 * 1.6  Combine the right side.
8x = 43.2    Divide by 8
x = 43.2 / 8
x = 5.4 pounds.    

If you take physics, you will do this quite frequently.