The free arm of a certain piece of equipment
moves on two steel balls. Unneeded info (I'm pretty sure.)
The radius of one of the steel balls is 2.25 cm more than the other ball.
The difference in their weights is 5650 g. Determine the radii of the balls.
The density of this steel is 8.15 g/cm3 .
Hint: Density = weight/volume.Actually, density = mass/volume **.
Smaller radius =
Larger radius =
Note: The following work leaves out needed units for the
sake of simplification of the solution.
Let r = the smaller radius
Let r + 2.25 = the larger radius.
Volume of larger steel ball = \(\displaystyle \dfrac{4}{3}\pi(r + 2.25)^3\)
Volume of smaller steel ball = \(\displaystyle \dfrac{4}{3}\pi r^3.\)
Note that mass = (density)(volume)
[from ** above]
Mass (of the larger steel ball) - mass (of the smaller steel ball) = 5650
becomes
\(\displaystyle (8.15)\bigg[\dfrac{4}{3}\pi (r + 2.25)^3\bigg] \ - \ (8.15)\bigg(\dfrac{4}{3}\pi r^3\bigg) \ = \ 5650\)
becomes
\(\displaystyle (8.15)\bigg(\dfrac{4}{3}\pi \bigg) \bigg[(r + 2.25)^3 - r^3)\bigg] \ = \ 5650\)
The quantity inside the brackets can be simplified and
show itself to be a second degree polynomial.
The whole equation amounts to one quadratic equation.
Note: If you wouldn't know a route to get it to as far as I did,
then I wouldn't expect you to be able to solve this quadratic
equation from here.
