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If the perimeter of a semi-circle is 4π + 8, what is the area of the s
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11 Jun 2021, 06:28
11 Jun 2021, 06:28
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If the perimeter of a semi-circle is 4π + 8, what is the area of the semi-circle?
A. 16π
B. 8π
C. 4π
D. 8
E. 4
A. 16π
B. 8π
C. 4π
D. 8
E. 4
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Re: If the perimeter of a semi-circle is 4π + 8, what is the area of the s
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11 Jun 2021, 06:29
11 Jun 2021, 06:29
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Carcass wrote:
If the perimeter of a semi-circle is 4π + 8, what is the area of the semi-circle?
A. 16π
B. 8π
C. 4π
D. 8
E. 4
A. 16π
B. 8π
C. 4π
D. 8
E. 4
Let r = the RADIUS of the circle
So, the length of the diameter = 2r
The circumference of an ENTIRE circle = 2πr
So, the circumference of a SEMIcircle = 2πr/2 = πr
We get:
So the PERIMETER = πr + 2r
We're told that the PERIMETER = 4π + 8
We can write: πr + 2r = 4π + 8
We can see that, if r = 4, the equation holds true
So, the radius must be 4
What is the area of the semi-circle?
Area of circle = πr²
So, area of SEMIcircle = πr²/2
So, the area of the given circle = π(4²)/2
= 16π/2
= 8π
Answer: B
Cheers,
Brent
If the perimeter of a semi-circle is 4 + 8, what is the area of the s
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21 Jan 2023, 12:25
21 Jan 2023, 12:25
Oh, nevermind, I found my mistake.
Hey, how did you find that the radius is 4?
I understand that you got it but just looking and run numbers in the head probably, but how can I get it mathematically, this is the part where I felt.
Let r = the RADIUS of the circle
So, the length of the diameter = 2r
The circumference of an ENTIRE circle = 2πr
So, the circumference of a SEMIcircle = 2πr/2 = πr
We get:
So the PERIMETER = πr + 2r
We're told that the PERIMETER = 4π + 8
We can write: πr + 2r = 4π + 8
We can see that, if r = 4, the equation holds true
So, the radius must be 4
What is the area of the semi-circle?
Area of circle = πr²
So, area of SEMIcircle = πr²/2
So, the area of the given circle = π(4²)/2
= 16π/2
= 8π
Answer: B
Cheers,
Brent
Hey, how did you find that the radius is 4?
I understand that you got it but just looking and run numbers in the head probably, but how can I get it mathematically, this is the part where I felt.
GreenlightTestPrep wrote:
Carcass wrote:
If the perimeter of a semi-circle is 4π + 8, what is the area of the semi-circle?
A. 16π
B. 8π
C. 4π
D. 8
E. 4
A. 16π
B. 8π
C. 4π
D. 8
E. 4
Let r = the RADIUS of the circle
So, the length of the diameter = 2r
The circumference of an ENTIRE circle = 2πr
So, the circumference of a SEMIcircle = 2πr/2 = πr
We get:
So the PERIMETER = πr + 2r
We're told that the PERIMETER = 4π + 8
We can write: πr + 2r = 4π + 8
We can see that, if r = 4, the equation holds true
So, the radius must be 4
What is the area of the semi-circle?
Area of circle = πr²
So, area of SEMIcircle = πr²/2
So, the area of the given circle = π(4²)/2
= 16π/2
= 8π
Answer: B
Cheers,
Brent
