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In the figure above, circles with centers A and B are

by M7MBA » Tue Apr 30, 2019 12:52 am

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In the figure above, circles with centers A and B are inscribed in rectangle JKLM. If the area of JKLM is 90, what is the area of the shaded region?

A. 90 − 9\(\pi\)
B. 90 − 15\(\pi\)
C. 90 − 18\(\pi\)
D. 90 − 36\(\pi\)
E. 90 − 72\(\pi\)

[spoiler]OA=C[/spoiler]

Source: Princeton Review
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by Jay@ManhattanReview » Tue Apr 30, 2019 8:22 pm
M7MBA wrote:Image
In the figure above, circles with centers A and B are inscribed in rectangle JKLM. If the area of JKLM is 90, what is the area of the shaded region?

A. 90 − 9\(\pi\)
B. 90 − 15\(\pi\)
C. 90 − 18\(\pi\)
D. 90 − 36\(\pi\)
E. 90 − 72\(\pi\)

[spoiler]OA=C[/spoiler]

Source: Princeton Review
The area of the shaded region = 90 - Area of two circles

To get the area of the circles, we need radius.

Since the area of the rectangle, JKLM is 90, we have KJ * KL = 90 => KJ * 15 = 90 => KJ = 6

Radius of the circle = KJ/2 = 6/2 = 3

Thus, area of a circle = π*3^2 = 9π

Thus, the area of two circles = 2*9Ï€ = 18Ï€

The area of the shaded region = 90 - 18Ï€

The correct answer: C

Hope this helps!

-Jay
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by swerve » Thu May 02, 2019 9:36 am
Since the area of the rectangle, \(JKLM\) is \(90\) and the length is \(15\)

Breadth \(= \frac{Area}{Length} = 6\)

This will be the diameter of both the circles with centers \(A\) and \(B\)

If the diameter is \(6\), the radius is \(3\)

Area of each circle \(= \pi * r^2 = 9\pi\)

Hence, area of both the circles are \(2*9\pi = 18\pi\)

Area of shaded region \(= \text{Area of rectangle} - \text{Area of both circles}\)
\(= 90 - 18\pi\) __C__
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by Scott@TargetTestPrep » Thu May 02, 2019 4:18 pm
M7MBA wrote:Image
In the figure above, circles with centers A and B are inscribed in rectangle JKLM. If the area of JKLM is 90, what is the area of the shaded region?

A. 90 − 9\(\pi\)
B. 90 − 15\(\pi\)
C. 90 − 18\(\pi\)
D. 90 − 36\(\pi\)
E. 90 − 72\(\pi\)

[spoiler]OA=C[/spoiler]

Source: Princeton Review
We are given that the length is 15, and since the area is 90, the width = diameter is 6, so the radius of each circle is 3.

Thus, the area of each circle is 3^2 x π = 9π, so the area of the two circles is 18π.

Finally, the area of the shaded region is 90 - 18Ï€.

Answer: C

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