OG Rectangle and Semicircle Q
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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!
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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
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
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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
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
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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
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