A geometry problem by Keerthi Reddy

Geometry Level 3

A railway train is travelling on a circular curve of perimeter $3000\times \dfrac{22}7$ meters at the rate of $66 \text{ km/hr}$ . Through what angle has it turned in 10 seconds?

\frac{11}{90}

radians

\frac{90}{11}

radians

\frac{56}{34}

degrees

\frac{11}{90}

degrees

\frac{90}{11}

degrees

1 solution

A Former Brilliant Member
Oct 16, 2017

$10~seconds=\dfrac{1}{360}~hour$ and $3000~meters=3~kilometers$

$distance=speed~\times~time=66 \times \dfrac{1}{360}=\dfrac{11}{60}$

Circumference, $c=2 \pi r$ $\implies$ $3\left(\dfrac{22}{7}\right)=2\left(\dfrac{22}{7}\right)r$ $\implies$ $r=\dfrac{3}{2}$

Arc length in radians, $L=r \theta$ $\implies$ $\dfrac{11}{60}=\dfrac{3}{2} \theta$ $\implies$ $\theta=$ $\boxed{\dfrac{11}{90}~radians}$

A geometry problem by Keerthi Reddy

1 solution

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