Maximum area = (1/2) * r^2 * sin(θ) = (1/2) * 5^2 * 1 = 25 cm².

Radius = diameter/2 = 20/2 = 10 cm.

Area = πr^2. If radius is doubled, new area = π(2r)^2 = 4πr^2, so area increases by a factor of 4.

Area ratio = (r1^2):(r2^2) = (4^2):(6^2) = 16:36 = 4:9.

Arc length = (θ/360) * 2πr = (60/360) * 2π(10) = (1/6) * 20π = 10.47 cm.

Area of sector = (θ/360) * πr² = (90/360) * π(5)² = (1/4) * 25π ≈ 6.25 cm².

Chord length = 2r * sin(θ/2) = 2 * 8 * sin(45°) = 8√2 cm.

Circumference = πd, so d = C/π = 31.4/π ≈ 10 cm.