OG Rectangle and Semicircle Q

AbeNeedsAnswers wrote:

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 + 2π

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*(πr^2) = 1/2*(π*2^2) = 2π 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]2π + 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.

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

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