Question

A wheel makes 720 revolutions in one minute. Through how many radians does it turn in one second?

Answer 1

$\textsf{Number of revolutions in 60sec/1min = 720}$

$\sf{Number \: of \: revolution \: in \: 1 sec = \frac{720}{60} } \\ \\ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 12}$

$\textsf{Angle made in 1 revolution = 360⁰} \\ \textsf{Angle made in 12 revolution = 12× 360⁰}$

$\boxed{ \sf{\footnotesize{\green{Radian \: measure = \frac{\pi}{180}×Degree \: Measure}}}}$

$\sf{Radians \: made \: in \: 6 \: revolutions = 12×360 × \frac{\pi}{180}} \\ \sf{= 12 × 2 × \pi} \\ \textsf {\large {\pink{= 24π}}} \\\textsf {\huge {\orange{= 75.398223686155}}}$

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Answer 2

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$\huge \bold{Question}$

A wheel makes 720 revolutions in one minute. Through how many radians does it turn in one second?

$\huge \bold{Solution}$

$\fbox \pink{Number of revolution in 60sec/1min = 720}$

$\small \sf\pink{Number \: of \: revolution \: in \: 1sec = \frac{ \cancel{720}}{ \cancel{60}} = 12 }$

Angel made in one revolution = 360°

Angel made in 12 revolution = 12×360° = 4,320

${\bold{\boxed {Radian \: measure \: = \frac{\pi}{180} × Degree \: Measure}}}$

Radian measure in 6 revolution

$\small 12 \times 360 \times \frac{\pi}{180} = 12 \times 2 \times \pi = 24\pi$

=> 75.398223686155

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