Mech. Engr.Problem

1. Apr 5, 2005

Robust

A mechanical engineer requires the turning of a circular disc giving an area of 16 units. What radius does he give the machinist?

2. Apr 5, 2005

FredGarvin

What is an equation for area that involves the radius?

You have the area...You have a constant $$\pi$$...

3. Apr 5, 2005

Robust

The equation I would give is: sqrt area/sqrt pi = radius; thus, if an area 16 then 4/1.77245....= 2.2567....radius. r^2*pi = 16 area

I took a bit of abuse by contempories for this formula - wanted to hear what Y'all might think of it.

4. Apr 5, 2005

brewnog

Looks good to me Robust.

Check that the given area is the cross sectional area, and not the total surface area of the disc. If this is so, you're spot on.

Don't be so quick to take abuse from contemporaries! Too many times I've lost face and backed down, only to find that I was right all along...

5. Apr 5, 2005

Robust

Thanks for the confirmation, but I'm not out of the woods yet on this, for the problem as originally given (project engineer) did state the total surface area, the tolerance being incidental. The PE is one of those who likes to throw these kinds of questions at us, just to keep us on our toes I suspect.

But the implications of this one does present a serious conflict as regards the pi value, showing it to be irrelevant. the radius is given consistently regardless of the pi pi value employed (recognized pi values). Here is the given formula: sqrt area/sqrt pi = radius; r^2*pi = 16 area!!

6. Apr 6, 2005

FredGarvin

I am not quite following you on this. All your PE is doing is restating the equation for the area of a circle in different ways. Nothing is different. Pi is Pi is Pi is Pi....

7. Apr 6, 2005

brewnog

If the PE is giving you the total surface area of the disc, this means you'll need to also know its thickness, - the total surface area comprising of two circular surfaces, and a 'strip' to go around the periphery.

8. Apr 6, 2005

Robust

It's a hypothetical question. the thickness and other parameters are immaterial. Only the radius to the circular plane is required.

9. Apr 6, 2005

brewnog

Robust.

Were you given the cross sectional area of the disc, in which case you're just rearranging the formula for the area of a circle, or were you given the total surface area of the disc.

If it's the latter, then the thickness is imperative, because you are considering two equal circular surfaces, and the 'strip' around the circumference. If the former is the case, your problem is pretty trivial, and Fred gave you the answer (in fact, you worked it out yourself!).

10. Apr 10, 2005

pack_rat2

Never before has so much discussion devolved from the simple formula, A = pi*r^2...;)

11. Apr 10, 2005

brewnog

I'm not nitpicking here am I?

12. Apr 11, 2005

Robust

Knitpicking is fine with me - probably the more the better!

13. Apr 19, 2005

Robust

Not so simple considering the absurdity of the area to a closed continuum described by other than a whole number or ending decimal.

14. May 1, 2005

BruceII

No mentor/ just a comon sense approach

I guess with questions concerning math problems, I go back to the basic formula. A=pi*r^2. Then simply factor it, to put the term you are looking for on the correct side of the = sign. r=sqrt(A/pi). A simple and basic approach to solving problems is always the best way to solve the problem. Any time a person tries to get out of their comfort zone, problems usually arise (wrong solution.) The best way to expand your comfort zone is to study study study. And, read forums like this to keep your mind open to the possibility that there may be more than approach to solving a problem. " Critical thinking starts with you."