Exploring Arc Length and Sector Area Applications

This video tutorial continues from part one, focusing on examples of arc length and sector area. It begins with converting degree measures to radians and then demonstrates how to calculate arc length and sector area using these conversions. The tutorial includes word problems and practical applications, emphasizing the importance of identifying whether a problem requires arc length or sector area calculations. The video concludes with examples and practice problems, providing solutions and encouraging viewers to pause and solve problems independently.

How do you convert 70 degrees to radians?

• 35 pi / 9

• 14 pi / 9

• 7 pi / 12

• 7 pi / 18

How is the arc length formula adjusted when dealing with radians instead of degrees?

• Divide central angle by 360 then multiply by 2 pi r

• Multiply radius by central angle in degrees

• Multiply radius by central angle

• No adjustment is needed

What is the formula to calculate the length of an arc?

• Radius squared times central angle

• One-half times radius squared times central angle

• Central angle divided by 360 times 2 pi r

• Radius times central angle

What is the formula for calculating the area of a sector?

• One-half times radius squared times central angle

• Radius squared times central angle

• Radius times central angle

• Central angle divided by 360 times pi r squared

What is the area of a sector formed by a 7 pi / 12 angle in a circle with a radius of 5?

• 35 pi / 9

• 175 pi / 24

• 70 pi / 18

• 14 pi / 9

For a 10 inch pizza cut into 8 slices, what is the central angle of one slice?

• 90 degrees

• 45 degrees

• 60 degrees

• 30 degrees

What keywords indicate a problem is asking for the arc length?

• Area, space inside

• Volume, capacity

• Length, distance, how far

• Square units, space

If a sprinkler waters grass at a 105-degree angle, how do you calculate the area it covers?

• 105 / 360 * pi r squared

• Radius squared times central angle

• One-half times radius squared times central angle

• Central angle over 360 times 2 pi r

What is the arc length if you travel halfway around the Earth, given its diameter?

• 24,873.6 miles

• 12,436.8 miles

• 6,218.4 miles

• 3,109.2 miles

How do you find the central angle for a clock's minute hand moving from 2 to 6?

• 45 degrees

• 60 degrees

• 90 degrees

• 120 degrees