BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

OG Rectangle and Semicircle Q

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 394
Joined: Sun Jul 02, 2017 10:59 am
Thanked: 1 times
Followed by:5 members

OG Rectangle and Semicircle Q

by AbeNeedsAnswers » Wed Jul 19, 2017 10:12 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Image

The window in the figure above consists of a rectangle and a semicircle with dimensions as shown. What is the area, in square feet, of the window?

A) 40 + 8ππ
B) 40 + 2ππ
C) 32 + 8ππ
D) 32 + 4ππ
E) 32 + 2Ï€

E
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Wed Jul 19, 2017 11:45 pm
AbeNeedsAnswers wrote:Image

The window in the figure above consists of a rectangle and a semicircle with dimensions as shown. What is the area, in square feet, of the window?

A) 40 + 8ππ
B) 40 + 2ππ
C) 32 + 8ππ
D) 32 + 4ππ
E) 32 + 2Ï€

E
The area of the window = Area of the semi-circle + Area of the rectangle

Area of the semi-circle = Half of the Area of the circle

It is given that the diameter of the semi-circle = 4 feet, thus the radius = 2 feet

Area of the semi-circle = 1/2*(Ï€r^2) = 1/2*(Ï€*2^2) = 2Ï€ sq feet

Area of the rectangle = Length x Breadth

It is given that Breadth = 4 feet and that the length + radius of the semi-circle = 10 feet.

Thus, the length of the rectangle = 10 - 2 = 8 feet

Thus, Area of the rectangle = Length x Breadth = 8 x 4 = 32 sq feet

=> The area of the window = Area of the semi-circle + Area of the rectangle = [spoiler]2Ï€ + 32 sq feet[/spoiler]

The correct answer: D

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Bangkok | Abu Dhabi | Rome | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Thu Jul 20, 2017 11:39 am
Hi AbeNeedsAnswers,

While there is a formal 'math' approach to this question - and the Official Explanation will provide it, there's a great way to use the answers against the prompt and minimize the work a little bit (as long as you know that the approximate value of pi = 3.14).

Since the window is NOT a gigantic rectangle, the area would have to be LESS than (10)(4) = 40, so we can eliminate Answers A and B immediately. Taking that idea a step further, you should be able to estimate the values of the remaining 3 answer choices (again, use pi = 3.14 as an approximation).

In Answer D: 32 + 4pi would be about 32 + 4(3.14) = 32 + 12.56 = 44.56... but this is greater than 40. Answer C would be even greater than Answer D (since 8pi is greater than 4pi), so neither of those answers can possibly be correct. That leaves just one option...

Final Answer: E

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Mon Jul 24, 2017 12:02 pm
I just want to add to Rich's explanation by saying....
The diagrams in problem solving questions are DRAWN TO SCALE unless stated otherwise.

So, as Rich has demonstrated, we can use this fact to solve the question through estimation.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

by Jeff@TargetTestPrep » Tue Jul 25, 2017 11:03 am
AbeNeedsAnswers wrote:Image

The window in the figure above consists of a rectangle and a semicircle with dimensions as shown. What is the area, in square feet, of the window?

A) 40 + 8ππ
B) 40 + 2ππ
C) 32 + 8ππ
D) 32 + 4ππ
E) 32 + 2Ï€
We are given a semicircle with a diameter of 4 ft., which also represents the width of the rectangle. We are also given that height of the window is 10 ft., which is the combined length of the radius of the semicircle and the length of the rectangle. To determine the length of the rectangle, we can subtract the radius of the semicircle, which is 2 ft., from the total length of 10 ft.:

10 - 2 = 8 ft.

Now we can calculate the area of the semicircle and the rectangle.

Area of semicircle = (1/2)Ï€(2^2) = 2Ï€

Area of rectangle = 8 x 4 = 32

Thus, the total area is 32 + 2Ï€.

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Post new topic Post Reply
• Page 1 of 1