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In the figure above, AC = BC = 8
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15 Jun 2021, 07:55
15 Jun 2021, 07:55
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Question Stats:
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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. \(32\pi-64\)
In the figure above, AC = BC = 8
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15 Jun 2021, 08:04
15 Jun 2021, 08:04
1
Solution:
When we divide a circle in to 4 equal parts the centre of the circle (360 degree) is also divides into 4 equal parts. Thus the above is a quarter of a circle.
And 8 is the radius of the circle.
Therefore, Area of the whole circle- \(πr^2\)=64π
To find the quarter of the circle, divide the area by 4=\(\frac{ 64π}{4}\)=16π
Now, we can find the area of the triangle= 32
Thus, the are of the shaded region= Area of the circle-Area of the triangle=16π-32
IMO B
Hope this helps!
When we divide a circle in to 4 equal parts the centre of the circle (360 degree) is also divides into 4 equal parts. Thus the above is a quarter of a circle.
And 8 is the radius of the circle.
Therefore, Area of the whole circle- \(πr^2\)=64π
To find the quarter of the circle, divide the area by 4=\(\frac{ 64π}{4}\)=16π
Now, we can find the area of the triangle= 32
Thus, the are of the shaded region= Area of the circle-Area of the triangle=16π-32
IMO B
Hope this helps!
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Joined: 10 Apr 2015
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Re: In the figure above, AC = BC = 8
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15 Jun 2021, 09:41
15 Jun 2021, 09:41
1
Carcass wrote:
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. \(32\pi-64\)
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
