Area and Arc Length Calculations

This video tutorial covers application problems involving arc length and sector area. It begins with an introduction to the concepts, followed by solving a problem about finding the diameter of a pie. The tutorial then moves on to calculating the total distance walked around a circular track. Next, it addresses clock-related problems, including calculating degrees moved by the minute hand and finding the area of a clock. The video concludes with multiple choice practice questions to reinforce understanding of arc length and sector area calculations.

If a pie is divided into six equal slices and the arc length of one slice is 5.4 cm, what is the diameter of the pie?

• 12.5 cm

• 10.31 cm

• 8.5 cm

• 15 cm

Tags

CCSS.7.G.B.4

Miss Noonan walked around a circular track with a radius of 40 meters four times. What is the total distance she walked?

• 400 meters

• 1280 meters

• 320 meters

• 1005.3 meters

Tags

CCSS.HSG.CO.A.1

CCSS.4.MD.C.5B

How many degrees does the minute hand of a clock move in 30 minutes?

• 90 degrees

• 120 degrees

• 180 degrees

• 240 degrees

Tags

CCSS.7.G.B.4

If the minute hand of a clock is 4 inches long, what is the area of the whole clock?

• 64π square inches

• 32π square inches

• 25π square inches

• 16π square inches

Tags

CCSS.HSG.C.B.5

What is the area of the sector created by the clock hands at two o'clock if the minute hand is 4 inches?

• 16π/3 square inches

• 24π/3 square inches

• 32π/3 square inches

• 8π/3 square inches

Tags

CCSS.HSG.C.B.5

What is the arc length of an arc with a central angle of 54 degrees and a radius of 10?

• 3π

• 5π

• 7π

• 9π

Tags

CCSS.HSG.C.B.5

In a circle with a radius of 16, what is the arc length of an arc with a central angle of 135 degrees?

• 21π

• 18π

• 15π

• 12π

Tags

CCSS.HSG.C.B.5

A sprinkler system covers a radius of 15 feet and rotates 100 degrees. What is the approximate area of grass watered?

• 225 square feet

• 196 square feet

• 150 square feet

• 250 square feet

Tags

CCSS.HSG.C.B.5

What is the formula for calculating the arc length of a circle?

• (Measure/360) × r²

• (Measure/360) × πd

• (Measure/360) × 2πr

• (Measure/360) × πr²

Tags

CCSS.HSG.C.B.5

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

• (Measure/360) × πd

• (Measure/360) × r²

• (Measure/360) × 2πr

• (Measure/360) × πr²

Tags

CCSS.HSG.C.B.5