Arc Length and Sector Area

Front

What is the formula for arc length?

Back

Arc Length (L) = (θ/360) × 2πr, where θ is the central angle in degrees and r is the radius.

Front

Define 'sector' in a circle.

Back

A sector is a portion of a circle enclosed by two radii and the arc between them.

Front

What is the formula for the area of a sector?

Back

Area of Sector = (θ/360) × πr², where θ is the central angle in degrees and r is the radius.

Front

If the radius of a circle is 7 cm and the central angle is 60°, what is the area of the sector?

Back

Area = (60/360) × π(7)² = (1/6) × 49π = 8.17 cm².

Front

What is the relationship between the circumference of a circle and arc length?

Back

Arc length is a fraction of the circumference, determined by the ratio of the central angle to 360°.

Front

Calculate the arc length of a circle with a radius of 10 cm and a central angle of 90°.

Back

Arc Length = (90/360) × 2π(10) = (1/4) × 20π = 5π cm.

Front

What is the circumference of a circle with a radius of 5 m?

Back

Circumference = 2πr = 2π(5) = 10π m.

Front

If the arc length is 15 cm and the radius is 10 cm, what is the central angle in degrees?

Back

θ = (Arc Length / Circumference) × 360 = (15 / 20π) × 360 = 86.18°.

Front

What is the area of a circle with a radius of 4 m?

Back

Area = πr² = π(4)² = 16π m².

Front

Define 'arc' in the context of a circle.

Back

An arc is a part of the circumference of a circle.