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

`(W1)/(W2) = (k r^3)/(k (r1)^3)`

Sub and solve
Begin by cancelling out the ks.

`(W1)/(W2) = (r^3)/((r1)^3)`

Next substitute for the 2 rs.

`(W1)/(W2) = (2^3)/(3^3)`

Now expand the 2 cubic amounts.

`(W1)/(W2) = (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

`(8)/(27) = (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.