What is the angle subtended at the centre of a circle of radius 6 cm by an arc of length 3 π cm?
We have
$r=6 \mathrm{~cm}$
length of the $\operatorname{arc}=3 \pi \mathrm{cm}$
We will find the angle subtended at the centre of a circle.
Length of the $\operatorname{arc}=\frac{\theta}{360} \times 2 \pi r$
Substituting the values we get,
$3 \pi=\frac{\theta}{360} \times 2 \pi \times 6$....(1)
Now we will simplify the equation (1) as below,
$3 \pi=\frac{\theta}{360} \times 12 \pi$
$3 \pi=\frac{\theta}{30} \times \pi$
$3=\frac{\theta}{30}$
$\Rightarrow \quad \theta=90^{\circ}$
Therefore, angle subtended at the centre of the circle is $90^{\circ}$.
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