Need help on this geometry concept question. At first it seems to be very easy, but i am missing something. Don't know what it is.
A semi-circular shaped window has diameter of 63 cm. Its perimeter equals:
(A) 126
(B) 162
(C) 198
(D) 251
(E) 221
Answer is B
Thanks
Sachin
A semi-circular shaped window has diameter of 63 cm
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- sachin_yadav
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The perimeter of a semi-circular shaped window involves adding the diameter of the semi-circle AND the circumference of the semi circle.sachin_yadav wrote:Need help on this geometry concept question. At first it seems to be very easy, but i am missing something. Don't know what it is.
A semi-circular shaped window has diameter of 63 cm. Its perimeter equals:
(A) 126
(B) 162
(C) 198
(D) 251
(E) 221
Answer is B
Thanks
Sachin
So, perimeter = diameter + (1/2)(pi)(diameter) [since it's half a circle]
= 63 + (1/2)(pi)(63)
IMPORTANT: At this point, before we perform tedious calculations, we should check the answer choices. Since they are nicely spread apart, we can estimate aggressively to get:
perimeter = 63 + about 100
= 163 (approx)
= B
Cheers,
Brent
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- Anju@Gurome
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sachin_yadav wrote:A semi-circular shaped window has diameter of 63 cm. Its perimeter equals:
Perimeter of the window = length of diameter + length of the circular arc = length of diameter + half of the perimeter of the circle = d + (Ï€d)/2, where d is the diameter of the circle
SO, perimeter = d + (Ï€d)/2
= 63 + π*63/2
= 63 + (22/7)*63/2 [As, π ≈ 22/7]
= 63 + 11*9
= 63 + 99
= 162
The correct answer is B.
Anju Agarwal
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Backup Methods : General guide on plugging, estimation etc.
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- sachin_yadav
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Brant and Anju, thank you for your replies.
Now i understand where i was making mistake. I wasn't adding the diameter with (1/2)(pi)(diameter)
Thank you once again
Sachin
Now i understand where i was making mistake. I wasn't adding the diameter with (1/2)(pi)(diameter)
Thank you once again
Sachin
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