SOLUTION: A wheat farmer is building a cylinder silo in which to store his grain. It needs to be 20m high, and he has 679m2 of steel to use. How wide will the silo be? I would just like t

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A wheat farmer is building a cylinder silo in which to store his grain. It needs to be 20m high, and he has 679m2 of steel to use. How wide will the silo be? I would just like t      Log On


   

Question 893193: A wheat farmer is building a cylinder silo in which to store his grain. It needs to be 20m high, and he has 679m2 of steel to use. How wide will the silo be?
I would just like the working please :)
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
How wide is really the diameter, which is two times the radius, r.
Total surface area for the cylinder, assuming top and bottom are included and ignoring any openings is %282pi%2Ar%29%2A20%2B2%28pi%2Ar%5E2%29=679.

Simplifying that,
40pi%2Ar%2B2pi%2Ar%5E2=679
2pi%2Ar%5E2%2B40pi%2Ar-679=0

General solution of quadratic equation, for r:
r=%28-40pi%2Bsqrt%281600pi%5E2%2B4%2A2pi%2A679%29%29%2F%284pi%29
r=%28-40pi%2B2sqrt%28400pi%5E2%2B2pi%2A679%29%29%2F%284pi%29
highlight%28r=-10%2B%281%2F%282pi%29%29sqrt%28400pi%5E2%2B2pi%2A679%29%29, or as whatever equivalent form you need.

Further, you wanted width, which is twice r; so you have width
highlight%28-20%2B%281%2Fpi%29sqrt%28400pi%5E2%2B2pi%2A679%29%29