A geometry problem by Mohammad Khaza

Geometry Level 3

If a central angle of 45 degree intersects an arc 6 inches long on the circumference of a circle ,what is the radius of the circle?

48//π 24/π 16 34

Mohammad Khaza by Mohammad Khaza , 20, Bangladesh

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2 solutions

Mohammad Khaza
Jul 21, 2017

for 45 degree the arc is=6inches long

so, for 1 degree the arc is = 6 45 \frac {6}{45} inches long

now, for 360 degree the arc is= 6 × 360 45 \frac {6\times 360}{45} inches long=48 inches

so, the circumference or 2πr=48

or, r= 48 2 π \frac{48}{2π} = 24 π \frac{24}{π}

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2πr is circumference, not Area.

Vaibhav Priyadarshi - 2 years, 11 months ago

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thanks. i have changed that.

Mohammad Khaza - 2 years, 10 months ago

The arc length is θ 360 \dfrac{\theta}{360} of the circumference of the circle. So we have

6 = 45 360 ( 2 π ) ( r ) 6=\dfrac{45}{360}(2 \pi)(r) ⟹ \color{#D61F06}\large \implies r = 24 π \color{#3D99F6}\boxed{r=\dfrac{24}{\pi}}

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