Raquel has created a program for a robot. The robot travels 10 meters and stops. The program is designed for wheels that are 2.5 cm in diameter. When Raquel replaces the wheels with ones having a 2.75 cm diameter, how should she adjust the number of rotations so that the robot travels the same distance?

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Raquel has created a program for a robot. The robot travels 10 meters and stops. The program is designed for wheels that are 2.5 cm in diameter. When Raquel replaces the wheels with ones having a 2.75 cm diameter, how should she adjust the number of rotations so that the robot travels the same distance?

Answer :

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calculista calculista · Answer 1 · 2025-03-21T18:59:21-04:00

Answer:

Raquel should adjust the number of rotations to 115.81 rotations

Step-by-step explanation:

step 1

Find the circumference of the wheels that are 2.5 cm in diameter

The circumference is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=2.5/2=1.25\ cm[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]C=2(3.14) (1.25)[/tex]

[tex]C=7.85\ cm[/tex]

step 2

Find the number of rotations

Divide 10 meters by the circumference

[tex]10\ m=1,000\ cm[/tex]

[tex]1,000/7.85=127.39\ rotations[/tex]

step 3

For a diameter of 2.75 cm find how should she adjust the number of rotations so that the robot travels the same distance

Find the circumference of the wheels

The circumference is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=2.75/2=1.375\ cm[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]C=2(3.14) (1.375)[/tex]

[tex]C=8.635\ cm[/tex]

step 4

Find the number of rotations

Divide 10 meters by the circumference

[tex]10\ m=1,000\ cm[/tex]

[tex]1,000/8.635=115.81\ rotations[/tex]