What is the perimeter of the shaded area, if the shape is a quarter circle with a radius of 8?
A) 2 pi
B) 4 pi
C) 2 pi + 16
D) 4 pi + 16
Is it C?
Nope.
The whole circumference is 2πr = 16π
And: 4pi
To find the perimeter of the shaded area, we need to find the circumference of the quarter circle.
The circumference of a circle is given by the formula:
C = 2πr
In this case, the radius (r) is given as 8. So we can substitute this value into the formula to find the circumference:
C = 2π(8)
C = 16π
But keep in mind that we only have a quarter (1/4) of a circle, so we need to find the perimeter of this quarter circle.
The perimeter of the quarter circle is equal to one-fourth of the circumference:
Quarter Circle Perimeter = (1/4) * 16π
Quarter Circle Perimeter = 4π
Comparing this with the given options:
A) 2π
B) 4π
C) 2π + 16
D) 4π + 16
We can see that the correct answer is B) 4π, as it matches the perimeter of the quarter circle.
To find the perimeter of the shaded area, we need to calculate the circumference of the quarter circle and the length of the straight line segment.
The circumference of a circle can be calculated using the formula 2 * pi * radius. In this case, the radius is given as 8, so the circumference of the quarter circle is (1/4) * (2 * pi * 8) = 4 * pi * 8 = 32 * pi.
The length of the straight line segment is equal to the radius of the quarter circle, which is 8.
To find the total perimeter, we sum up the circumference of the quarter circle and the length of the straight line segment: (32 * pi) + 8.
Now, let's compare this value with the answer choices given:
A) 2 pi: This is not correct because 2 pi would represent the circumference of a full circle, not a quarter circle.
B) 4 pi: This is not correct either because it only considers the quarter circle's circumference and does not include the length of the straight line segment.
C) 2 pi + 16: This is also not correct because it does not take into account the circumference of the quarter circle.
D) 4 pi + 16: This is the correct answer because it includes the circumference of the quarter circle (32 * pi) as well as the length of the straight line segment (8).
Therefore, the correct answer is D) 4 pi + 16.