Exploring Arc Length and Sector Area in Radians

What is the radian measure equivalent of 200 degrees?

• π/2 radians

• 10π/9 radians

• 200π/180 radians

• 20π/18 radians

What is the radian measure equivalent of 315 degrees?

• 5π/3 radians

• 7π/4 radians

• 315π/180 radians

• 63π/36 radians

How do you calculate the arc length of a circle?

• Radius + Central Angle

• 2πr × (Central Angle/360)

• πr^2 × (Central Angle/360)

• Radius × Central Angle

If the radius of a circle is 12 and the central angle is 2π/3, what is the arc length?

• 8π

• 24π

• 4π

• 12π

Given an arc length of 30 and a radius of 14, what is the angle in radians?

• π radians

• 30/14 radians

• 2π/7 radians

• 15/7 radians

Given an arc length of 310 and a radius of 100, what is the angle in radians?

• π radians

• 3.1 radians

• 310/100 radians

• 31/10 radians

What formula is used to calculate the sector area in radians?

• θ/2 × r^2

• 2πr × (θ/360)

• θ × r^2

• πr^2 × (θ/360)

What is the sector area if θ = 2π/3 and radius = 12?

• 72π cm^2

• 144π cm^2

• 24π cm^2

• 48π cm^2

How do you find the radius of a circle given the sector area and angle?

• Sector Area × 2/θ

• Square root of (Sector Area × 2/θ)

• Sector Area / (π × θ)

• Square root of (Sector Area / (θ/2))

To find the radius of a circle with a sector area of 150 square meters and θ = 3π/4, what is the radius?

• 9.8 meters

• 10.5 meters

• 11.3 meters

• 12.5 meters