A semi-circular shaped window has diameter of 63 cm

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sachin_yadav: Master | Next Rank: 500 Posts; Posts: 212; Joined: Mon Dec 06, 2010 12:52 amFollowed by: 1 member; Location: India; Thanked: 5 times

by sachin_yadav » Fri Apr 26, 2013 9:33 pm

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

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Source: Beat The GMAT — Problem Solving | Fri Apr 26, 2013 9:33 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Apr 26, 2013 9:42 pm

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

The perimeter of a semi-circular shaped window involves adding the diameter of the semi-circle AND the circumference of the semi circle.

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

Brent Hanneson - Creator of GMATPrepNow.com

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Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

by Anju@Gurome » Fri Apr 26, 2013 9:47 pm

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 + Ï€*63/2
= 63 + (22/7)*63/2 [As, Ï€ â‰ˆ 22/7]
= 63 + 11*9
= 63 + 99
= 162

The correct answer is B.

Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
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sachin_yadav: Master | Next Rank: 500 Posts; Posts: 212; Joined: Mon Dec 06, 2010 12:52 amFollowed by: 1 member; Location: India; Thanked: 5 times

by sachin_yadav » Fri Apr 26, 2013 9:57 pm

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

Never surrender

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