1.what is the area of a sector with a central angle of 160 degrees and a diameter of 5.8m? round the answer to the nearest tenth
A. 8.1 m^2
B.4.0 m^2
C.47.0 m^2
D.11.7 m^2
2.what is the area of a regular octagon with a side of 8 in round the answer to the nearest tenth.
A 443.4in^2
B. 618.0in^2
C. 221.7 in^2
D. 309.0 in^2
the area is 1/2 r^2 θ
= 1/2 * 2.9^2 * 160/180 π
= 11.74
The central angle of an octagon is 45°.
area = 1/2 apothem * perimeter
= 1/2 (4/tan 22.5°) * 8*8
= 309.0
correct
What is the answer to this example:The area of circle PQR with centre O is 72cmsquare.what is the area of sector POQ if POQ=40degree?(WAEC) question
1. 60cm
2. m<1=36,m<2=144
3. 13/3 and 169/9
4. 172.0 in
5. 162
6. 26pi in
7. 23.04pi
8. 11.7 m
9. (120pi+36(square root)3) m
All of your answers seem to be correct! Great job!
1. Well, the first thing we need to do is find the radius. Since the diameter is given as 5.8m, the radius would be half of that, which is 2.9m. Now we can find the area of the sector. The formula for the area of a sector is (central angle/360) * π * radius^2. So, for this sector, the area would be (160/360) * π * (2.9^2). Doing the math, we get approximately 11.7 m^2. Therefore, the answer is D. 11.7m^2.
2. Let's use a little humor to tackle this problem. So, we have a regular octagon with a side length of 8 inches. The area of an octagon can be found by using the formula (2 * (1 + √2)) * s^2, where s is the side length. If we plug in the given side length of 8 inches, we get (2 * (1 + √2)) * 8^2. After some math magic, we get approximately 309.0 in^2. So, the answer is D. 309.0 in^2. Now that's a lot of octagonal goodness!
To find the area of a sector, you can use the formula:
Area = (θ/360) * π * r^2
where θ is the central angle in degrees, π is a constant approximately equal to 3.14159, and r is the radius of the sector.
1. Given that the central angle is 160 degrees and the diameter is 5.8m, we can find the radius by dividing the diameter by 2: r = 5.8m / 2 = 2.9m.
Now, substitute the values into the formula:
Area = (160/360) * π * (2.9)^2
= (4/9) * 3.14159 * 8.41
≈ 11.7 m^2
Therefore, the answer is D. 11.7 m^2.
2. To find the area of a regular octagon, you can use the formula:
Area = 2 * (1 + √2) * s^2
where s is the length of each side of the octagon.
Given that the side length is 8 in, substitute it into the formula:
Area = 2 * (1 + √2) * (8)^2
= 2 * (1 + 1.41421) * 64
≈ 309.0 in^2
Therefore, the answer is D. 309.0 in^2.