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

Redeem

What is the area of the region of diagram?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

What is the area of the region of diagram?

by Max@Math Revolution » Mon May 02, 2016 10:46 pm
What is the area of the region of diagram?

A. 8+(3Ï€/2)
B. 10+(3Ï€/2)
C. 8+3Ï€
D. 10+3Ï€
E. 8+6Ï€

* A solution will be posted in two days.
Attachments
4.png
Top
Source: — Problem Solving |
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

by Max@Math Revolution » Sun May 08, 2016 5:55 pm
As you can see from the figure attached, we have a rectangle that has an area of 4*2=8 and 2*1=2. Also, there are three semicircles with 1 as their radii. All together, the area is 8+2+3(Ï€/2)= 10+(3Ï€/2). Hence, B is the correct answer.
Top
Master | Next Rank: 500 Posts
Posts: 199
Joined: Sat Apr 26, 2014 10:53 am
Thanked: 16 times
Followed by:4 members
GMAT Score:780

by 800_or_bust » Sun May 08, 2016 7:26 pm
Max@Math Revolution wrote:What is the area of the region of diagram?

A. 8+(3Ï€/2)
B. 10+(3Ï€/2)
C. 8+3Ï€
D. 10+3Ï€
E. 8+6Ï€

* A solution will be posted in two days.
First let's determine the area of each semi-circular region. The area of a circle is equal to π(r^2). Here, r=1 so the area of any given full circle of radius 1 would be equal to π. However, we have three semi (half) circles. Therefore, the area of each semi-circle is π/2. And since we have 3 of them, the total area of the semicircular regions is 3π/2.

Next, turning to the rectangular region. The larger rectangle at top is 4 units in width, and the length is 2 units (equal to the diameter of the semicircles). So, the area of this rectangle is 8. The smaller rectangle has width of 2 units (equal to the diameter of the semicircle). The length of this rectangle is a little more challenging, as the line segment of length 2 extends into the upper rectangular region. So we need to subtract the radius of the semicircle to avoid double counting. Therefore, the uncounted length is equal to 1. And the area of this rectangle is simply 2.

Adding up the two rectangles and three semicircles, we get 10+3Ï€/2.
800 or bust!
Top
Post new topic Post Reply
• Page 1 of 1