Circumference: $C = 2\pi r = 2\pi(5) = 10\pi$

Area: $A = \pi r^2 = \pi(5)^2 = 25\pi$

Answer: Circumference = $10\pi$ (or ≈ 31.4), Area = $25\pi$ (or ≈ 78.5)

Step 1: Find the radius $r = \frac{d}{2} = \frac{16}{2} = 8$

Step 2: Use arc length formula $\text{Arc length} = \frac{\theta}{360°} \times 2\pi r$

$= \frac{45}{360} \times 2\pi(8)$

$= \frac{1}{8} \times 16\pi$

$= 2\pi$

Answer: Arc length is $2\pi$ (or ≈ 6.28)

Draw a radius to the chord's endpoint and a perpendicular from center to chord.

This creates a right triangle:

• Hypotenuse = radius = 10
• One leg = distance from center = 8
• Other leg = half the chord length

Use Pythagorean Theorem: $8^2 + \left(\frac{c}{2}\right)^2 = 10^2$

$64 + \frac{c^2}{4} = 100$

$\frac{c^2}{4} = 36$

$c^2 = 144$

$c = 12$

Answer: The chord length is 12 cm