# Thread: radius etc

1. ## radius etc

I have a question i need some help on please,

A factory produces metal discs of radius (r - 1) mm and of negligible thickness for making washers and metal spheres of radius r mm for ball bearings. THe total surface area of a disc (both sides) and a ball bearing is 132 (pie) mm(squared). Calculate r

thank you

2. Hello, Kim!

A factory produces metal discs of radius (r - 1) mm of negligible thickness
and metal spheres of radius r mm.
The total surface area of a disc (both sides) and a ball bearing is 132π mm²
Calculate r.
You're expected to know some area formulas.

. . Area of circle with radius r: .A .= .πr²

. . Area of sphere with radius r: .A .= .4πr²

The disc has a total area of: .2·π(r - 1)²

The sphere has an area of: .4πr²

The total area is 132π: . 2π(r - 1)² + 4πr² .= .132π

Divide by 2π: . (r - 1)² + 2r² .= .66

We have a quadratic: . 3r² - 2r - 65 .= .0

. . which factors: . (r - 5)(3r + 13) .= .0

. . and has roots: . r .= .5, -13/3

Since the radius must be positive: .r = 5