A circle's center is at $(3, 5)$ $(3 ,5 )$ and it passes through $(2, 2)$ $(2 ,2 )$ . What is the length of an arc covering $\frac{5 π}{4}$ $(5pi ) /4$ radians on the circle?

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A circle's center is at $(3, 5)$ $(3 ,5 )$ and it passes through $(2, 2)$ $(2 ,2 )$ . What is the length of an arc covering $\frac{5 π}{4}$ $(5pi ) /4$ radians on the circle?

1 Answer

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Answer 1 · 2016-06-15T01:44:31

$12.4 u n i t$ $12.4unit$

Explanation:

The radius of the circle $R$ $R$ is the distance between its center $(3, 5)$ $(3,5)$ to the point $2, 2)$ $2,2)$ on it.
So $R = \sqrt{{(3 - 2)}^{2} + {(5 - 2)}^{2}} = \sqrt{10}$ $R=sqrt((3-2)^2+(5-2)^2)=sqrt10$

If the length of the arc which subtends angle $5 \frac{π}{4}$ $5pi/4$ at the center of the circle is S,then

$\frac{S}{R} = 5 \frac{π}{4}$ $S/R=5pi/4$

$S = \sqrt{10} \times \frac{5}{4} \times 3.14 = 12.4 u n i t$ $S=sqrt10xx5/4xx3.14=12.4 unit$

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A circle's center is at $(3, 5)$ $(3 ,5 )$ and it passes through $(2, 2)$ $(2 ,2 )$ . What is the length of an arc covering $\frac{5 π}{4}$ $(5pi ) /4$ radians on the circle?

1 Answer

Explanation:

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1 Answer

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A circle's center is at $(3, 5)$ $(3 ,5 )$ and it passes through $(2, 2)$ $(2 ,2 )$ . What is the length of an arc covering $\frac{5 π}{4}$ $(5pi ) /4$ radians on the circle?