Problem Solving

Seems easy but my ultimate answer differed from the original.

Area = (pi) r^2 - (pi) (r - s)^2

= (pi)(r - r + s)(r + r - s) [Since (a^2 - b^2 = (a - b)(a + b))]
= (pi)(s)(2r - s)

Using the backsolving method, I am getting B for an answer.

Am I doing something wrong?

I plugged in 8 for the radius of the medallion and 3 for the distance of the frame...and B is the only answer that matches if you subtract...

From the question we can find:

Area of Metal Frame = (phi)r^2 - (phi) (r-s)^2

= (phi)r^2 - (phi) (r^2 - 2rs + s^2)
= (phi)r^2 - (phi)r^2 + 2(phi)rs - (phi)s^2
= 2(phi)rs - (phi)s^2
= (phi)s (2r - s)

Hence the answer is D (CMIIW ya)

Hope this helps...Enjoy your day

lightbulb wrote:Area = (pi) r^2 - (pi) (r - s)^2

= (pi)(r - r + s)(r + r - s) [Since (a^2 - b^2 = (a - b)(a + b))]
= (pi)(s)(2r - s)

What made you realize that "r" is the radius of the complete circle, encompassing the non shaded region and the shaded region? I thought r was radius of the the non shaded circle and s is the width of the frame(width of the shaded frame). So (r+s) was the complete circle radius. Appreciate your response.

btw, the answer is E.

Not quite understanding why you are subtracting s from r. The total radius is r+s. Wouldn't that give the total radius? Then you would subtract non shaded area which is r & then you would get answer. My calculation:

Pi(r+s)^2-pir^2 => radius of whole cir - radius on inner cir

I get = pi s(2r+s)

Any clarification would be helpful

The figure shows the TOP SIDE of a circular medallion made by a CIRCULAR piece of glass surrounded by a metal frame represented by the shaded region. In other words, the top side is the metal frame with width S. The back side= the cercle with radius r.


pi(r-s)^2= Area of unshaded region.
pi(r)^2= Area of the ushaded + shaded region

subtracting these two you get the result

The others did a good job explaining as well so I will not go over the calculations.

I hope it helped

Not quite understanding why you are subtracting s from r. The total radius is r+s. Wouldn't that give the total radius? Then you would subtract non shaded area which is r & then you would get answer. My calculation:

Pi(r+s)^2-pir^2 => radius of whole cir - radius on inner cir

I get = pi s(2r+s)

Any clarification would be helpful

ildude02 wrote:

lightbulb wrote:Area = (pi) r^2 - (pi) (r - s)^2

= (pi)(r - r + s)(r + r - s) [Since (a^2 - b^2 = (a - b)(a + b))]
= (pi)(s)(2r - s)

What made you realize that "r" is the radius of the complete circle, encompassing the non shaded region and the shaded region? I thought r was radius of the the non shaded circle and s is the width of the frame(width of the shaded frame). So (r+s) was the complete circle radius. Appreciate your response.

btw, the answer is E.

There is a lot of confusion about which answer is correct. I got the point that r is the radius of the entire medallion and and s which is actually part of the medallion.

Therefore E is the answer.

Now it would be nice if could post the OA, so there is no confusion.

Anyways I am also getting B as the answer when I plugged in numbers.

Thanks dude

parrallel_chase

you are correct..statement says the medallion has radius of "r" and the medallion consist of glass and a metal ring (which is "s" in thicknes)

could you show your work so I can get a better understanding.

thanks