Pulleys and Tangent Segments

This lesson covers the calculation of the total length of a belt tied around two pulleys. It begins with an introduction to the setup, including the radii of the pulleys and the distance between them. The lesson explains the concept of tangents and parallel lines, followed by calculations involving circles and radii. The Pythagorean theorem is applied to find certain lengths, and arc lengths are calculated using given angles. The lesson concludes with the final calculation of the total belt length.

What is the main objective of the lesson?

• To measure the height of a building

• To find the volume of a cylinder

• To calculate the area of a circle

• To determine the length of a belt around two pulleys

What are the radii of the pulleys with centers A and B?

• 15 cm and 10 cm

• 5 cm and 2.5 cm

• 20 cm and 10 cm

• 10 cm and 5 cm

What is the distance between the centers of the two pulleys?

• 50 cm

• 100 cm

• 25 cm

• 75 cm

What is the angle SAB equal to?

• 84.26 degrees

• 90 degrees

• 60 degrees

• 45 degrees

What theorem is used to calculate the length of the tangent segments?

• Fermat's Last Theorem

• Thales' theorem

• Binomial theorem

• Pythagorean theorem

What is the length of the tangent segment SR?

• 49.75 cm

• 55 cm

• 50 cm

• 45 cm

How is the arc length RQ calculated?

• Using the angle at the center and the radius

• By measuring directly

• By estimating visually

• Using the diameter and circumference

What is the total length of the belt?

• 150 cm

• 140 cm

• 160 cm

• 147.64 cm