Question

The amount of material needed to cover a ball varies directly with the square of the radius. It takes about 221.63 cm2 of material to cover a ball with a radius of 4.2 cm. What is the radius of a ball that needs 352.92 cm2 of material to cover it?

Answer 1

`r=5.3 cm`

Explanation:

Since the amount of material necessary to cover the ball varies directly with the square of the radius, we know

`4.2^2 prop 221.63`
Or: `4.2^2 = k*221.63` where k is some constant

Now we want to find `r_2` such that `(r_2)^2 = k*352.92`

We could solve for k and then plug in, but a simpler method would be to divide our equations and solve for `r_2` directly:

`4.2^2 / (r_2)^2 = (k*221.63)/(k*352.92)`

Notice how the k's cancel out, and we can solve for `r_2` directly.

`4.2^2*352.92 = (r_2)^2*221.63`

`(4.2^2*352.92) / 221.63 = (r_2)^2`

`r_2 = sqrt((4.2^2*352.92)/221.63)`

`r_2 = 5.3 cm`