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)
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geometry
Source: Beat The GMAT — Problem Solving |
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...
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
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
Life is about choices
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.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)
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
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
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
Alin Sigheartau
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
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
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.ildude02 wrote: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.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)
btw, the answer is E.
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
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
