Question

A wheel makes 8 revolutions in one minute. Through how many

radians does it turn in 10 minutes?​

Answer 1

Given that:

• A wheel makes 8 revolutions in one minute.

To Find:

• Through how many radians does it turn in 10 minutes?

As we know:

• Radian measure = (π × Degree measure)/180°

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:

• Degree measure = 360° × 80

↣ Radian measure = (π × 360 × 80)/180

↣ Radian measure = π × 2 × 80

↣ Radian measure = 160π

Hence,

• A wheel turns 160π radian in 10 minutes.

Answer 2

Answer:

Given :-

• A wheel makes 8 revolution in one minute.

To Find :-

• How many radians does it turn in 10 minutes.

Formula Used :-

$\clubsuit$ Radian Formula :

$\mapsto \sf \boxed{\bold{\pink{Radian =\: \bigg\lgroup \dfrac{\pi}{180^{\circ}} \times Degree\bigg\rgroup}}}$

Solution :-

Given :

$\mapsto$ 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 :

$\implies \sf 8 \times 10$

$\implies \sf\bold{\purple{80\: revolutions}}$

Now, as we know that :

$\leadsto \sf\bold{1\: revolution =\: 360^{\circ}}$

Hence, 80 revolution will be :

$\implies \sf 80\: revolution =\: 360^{\circ} \times 80$

$\implies \sf\bold{\purple{80\: revolution =\: 28800^{\circ}}}$

Given :

$\bigstar\: \: \bf{Degree =\: 28800^{\circ}}$

According to the question by using the formula we get,

$\longrightarrow \sf Radian =\: \dfrac{\pi}{180^{\circ}} \times 28800^{\circ}$

$\longrightarrow \sf Radian =\: \dfrac{2880\cancel{0}^{\circ}\pi}{18\cancel{0}^{\circ}}$

$\longrightarrow \sf Radian =\: \dfrac{\cancel{2880^{\circ}}\pi}{\cancel{18^{\circ}}}$

$\longrightarrow \sf Radian =\: \dfrac{160\pi}{1}$

$\longrightarrow \sf\bold{\red{Radian =\: 160\pi}}$

${\small{\bold{\underline{\therefore\: The\: radian\: does\: it\: takes\: in\: 10\: minutes\: is\: 160\pi\: .}}}}$