The answer is diameter: 32 in, area: 64 in²
The perimeter of a sector of a circle is:
P = 2r + l
l = r<span>θ
P = 2r + r</span>θ<span>
P = 32 in
32 = 2r + r</span><span>θ
</span>32 - 2r = r<span>θ
</span>θ = (32 - 2r)/r
θ = (2*16 - 2*r)/r
θ = 2(16 - r)/r<span>
Area of the sector of the circle is:
A = r</span>²/2 * θ
A = r²/2 * 2(16 - r)/r
A = r² * (16 - r)/r
A = r(16 - r)
A = 16r - r²
For the maximum area:
A' = 16 - 2r
A' = 0
16 - 2r = 0
16 = 2r
r = 8 in
The diameter (D) of the circle is twice of the radius:
D = 2r = 2 * 8 = 16 in
The maximum area is:
A = 16r - r²
r = 8 in
A = 16 * 8 - 8²
A = 128 - 64
A = 64 in²
Answer:
A≈706.86ft²
Step-by-step explanation:
A=πr2=π·152≈706.85835ft²
rounded two decimal places= 706.86
Answer:
Please refer to the attachment
4,000
I know this because 2,000 • 2 = 4,000
