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?

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Answer 1 · 2016-09-29T18:58:51

$r=5.3 cm$

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.

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

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

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

$r_2 = 5.3 cm$