A wheel makes 8 revolutions in one minute. Through how many
radians does it turn in 10 minutes?
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A wheel makes 8 revolutions in one minute. Through how many
radians does it turn in 10 minutes?
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Given that:
To Find:
As we know:
We have:
∵ Number of revolution in one minute = 8
∴ Number of revolution in 10 minutes = 8 × 10 = 80
We know:
∵ 1 revolution = 360°
∴ 80 revolutions = 360° × 80
Now we have:
↣ Radian measure = (π × 360 × 80)/180
↣ Radian measure = π × 2 × 80
↣ Radian measure = 160π
Hence,
Answer:
Given :-
To Find :-
Formula Used :-
[tex]\clubsuit[/tex] Radian Formula :
[tex]\mapsto \sf \boxed{\bold{\pink{Radian =\: \bigg\lgroup \dfrac{\pi}{180^{\circ}} \times Degree\bigg\rgroup}}}\\[/tex]
Solution :-
Given :
[tex]\mapsto[/tex] A wheel makes 8 revolution in one minute.
It's means, a wheel can makes 8 revolution in one minute.
Then, in 10 minutes a wheel can makes :
[tex]\implies \sf 8 \times 10[/tex]
[tex]\implies \sf\bold{\purple{80\: revolutions}}[/tex]
Now, as we know that :
[tex]\leadsto \sf\bold{1\: revolution =\: 360^{\circ}}[/tex]
Hence, 80 revolution will be :
[tex]\implies \sf 80\: revolution =\: 360^{\circ} \times 80[/tex]
[tex]\implies \sf\bold{\purple{80\: revolution =\: 28800^{\circ}}}[/tex]
Given :
[tex]\bigstar\: \: \bf{Degree =\: 28800^{\circ}}[/tex]
According to the question by using the formula we get,
[tex]\longrightarrow \sf Radian =\: \dfrac{\pi}{180^{\circ}} \times 28800^{\circ}[/tex]
[tex]\longrightarrow \sf Radian =\: \dfrac{2880\cancel{0}^{\circ}\pi}{18\cancel{0}^{\circ}}[/tex]
[tex]\longrightarrow \sf Radian =\: \dfrac{\cancel{2880^{\circ}}\pi}{\cancel{18^{\circ}}}[/tex]
[tex]\longrightarrow \sf Radian =\: \dfrac{160\pi}{1}[/tex]
[tex]\longrightarrow \sf\bold{\red{Radian =\: 160\pi}}[/tex]
[tex]{\small{\bold{\underline{\therefore\: The\: radian\: does\: it\: takes\: in\: 10\: minutes\: is\: 160\pi\: .}}}}\\[/tex]