What is the radius if the area of the circle is:
4x^2(PI)
My answer 4x^2(pi)=(pi)(r)(2), 16x(pi)=(pi)(r)(2), 16x/pi=5x.
5(PI)
My answer 5(pi)=(pi)(r)(2), sqare root of 5 is 2.23, which rounds to 3, 3(pi)=square root of 9.
What is the area of the sector if the radius is 6 and the degree measure is:
30
My answer 30/360(pi)(6)^2, 0.83(pi)(36),rounds to 1(pi).
50
My answer 50/360[(pi)6^2], 7.1/72[(pi)36], 7.1(36), 255/3.14, =81, square root of 81=9*pi.
90
My answer 90/360[(pi)6^2] 9.49/72[(pi)(36)], 18/9=2*pi.
120
My answer 120/360[(pi)6^2], 4/72[(pi)(36)] 4(36)=144, square root of 144=12*pi.
These are the question and answers that were incorrect on my assignment. I am unsure of what I did incorrect. I would be grateful for assistance. Cheers!
Sincerely,
Marisa
first one:
πr^2 = 4x^2 π
r^2 = 4x2
r = 2x
if area = 5P
πr^2 = 5π
r^2 = 5
r = √5
sector angle=60°, r = 6
area = (30/360)(π)(36) = 3π
for sector angle=50°
area = (50/36)(36π) = 5π
the rest are the same
Hi Marisa! I'd be happy to help you understand where you went wrong with your answers. Let's go through each question and see how to find the correct answers step by step.
1. What is the radius if the area of the circle is 4x^2(PI)?
To find the radius, we need to use the formula for the area of a circle, which is A = πr^2. In this case, the area is given as 4x^2(PI), so we can set up the equation as:
4x^2(PI) = πr^2
Divide both sides by π: 4x^2 = r^2
Take the square root of both sides: √(4x^2) = √(r^2)
Simplify: 2x = r
So, the radius is 2x, not 5x as you calculated.
2. What is the area of the sector if the radius is 6 and the degree measure is 30?
To find the area of a sector, we need to use the formula: A = (θ/360) * πr^2, where θ is the degree measure of the sector.
For this question, the radius is given as 6 and the degree measure is 30, so we can plug these values into the formula:
A = (30/360) * π * 6^2
Simplify: A = (1/12) * π * 36
A = 3π square units
So, the correct answer is 3π, not 1π as you calculated.
3. For the degree measure of 50 degrees and 90 degrees, your calculations are correct. The area of the sector with a 50-degree measure is (1/9)π square units, and for a 90-degree measure, it is (1/3)π square units.
4. What is the area of the sector if the radius is 6 and the degree measure is 120?
To find the area of the sector, we use the same formula: A = (θ/360) * πr^2
For this question, the radius is given as 6 and the degree measure is 120, so we can plug these values into the formula:
A = (120/360) * π * 6^2
Simplify: A = (1/3) * π * 36
A = 12π square units
So, the correct answer is 12π, not 144 as you calculated.
I hope this clears up any confusion you had. If you have any more questions, feel free to ask!