In the figure above, AC = BC = 8, angle C = 90°, and the circular arc

Question

https://gmatclub.com/forum/download/file.php?id=25841 In the figure above, AC = BC = 8, angle C = 90°, and the circular arc has its center at point C. Find the area of the shaded region. A. 8\pi-32 B. 16\pi-32 C. 16\pi-64 D. 32\pi-32 E. 32\pi-64 Kudos for a correct solution . gm-tuaaof_img1.png

BrentGMATPrepNow · Accepted Answer

Area of shaded region = ( area of sector ) - ( area of triangle )

Area of circle = π(radius)²
Area of triangle = (base)(height)/2

The sector ABC is 1/4 of a circle of radius 8
So,  area of sector = (1/4)(π)(8²)
= 16π

area of triangle = (8)(8)/2
= 32

So, area of shaded region = ( 16π ) - ( 32 )

Answer: B

Cheers,
Brent

iamdp · Answer

Hi

Area of sector = (90/360)*pi(8^2) = 16pi

Area of triangle = (1/2)*8*8 = 32

Area of shaded region = area of sector - area of triangle = 16pi-32

lipsi18 · Answer

Area of shaded region = (area of circle/4) - area of triangle = (pi* 8^2)/4 - (8*8/4) = 16 pi - 32
Therefore answer is B

Thanks,

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION:

There’s not a single formula we can use to get the answer, but by combining a few formulas, we can calculate this.

First, think about the circle. The circle has radius r = 8, so its total area would be  A=\pi{r^2}=64\pi .
gm-tuaaof_img5

This entire figure is a quarter of the circle, so that area would be  quarter \ circle=16\pi .

Now, the shaded area (technically known as a circular segment), would have an area of
(circular segment) = (quarter circle) – (triangle ABC)

Well, we already have the area of the quarter circle. The triangle would have an area of (1/2)bh = 32. Therefore, the area of the segment is  area=16\pi-32 .

Answer = (B)

In the figure above, AC = BC = 8, angle C = 90°, and the circular arc

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In the figure above, AC = BC = 8, angle C = 90°, and the circular arc

Prep Toolkit

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