Page 150 - Math Course 3 (Book 2)

Circles: Parts and Circumference

Let’s Begin

Find Circumference, Diameter, and Radius Use Other Figures to Find Circumference

Example Example

Find C if r = 13 inches. Find the exact circumference of ⊙K.

C = 2πr Circumference formula
= 2π(13) Substitution 3√2
= 26π or about 81.68

Answer 26π or ≈ 81.68 in. K

Find C if d = 6 millimeters.

C = 2πr Circumference formula The radius of the circle is the same length as
= 2π(6) Substitution either leg of the triangle. The legs of the triangle
= 6π or about 18.85 have equal length. Call the length x.

Answer 6π or ≈ 18.85 mm a² + b² = c² Pythagorean Theorem

Find d and r to the nearest hundredth if C = 65.4 x² + x² = (3√2)² Substitution
feet.

C = πd Circumference formula 2x² = 18 Simplify.
65.4 = πd Substitution
65.4 Divide each side by π. x² = 9 Divide each side by 2.
π = d
20.82 ≈ d Use a calculator. Take the square root of each
1 x = 3 side.
= (20.82) Radius formula
2
1
≈ (20.82) d ≈ 20.82 So the radius of the circle is 3.
2
≈ 10.41 ft Use a calculator. C = 2πr Circumference formula.
C = 2π(3) or 6π. Substitution.

Answer d ≈ 20.82 ft; r ≈ 10.41 ft Answer 6π

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