A sector in a pie graph is 12 cm^2, radius is 4cm, what is the angle?

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A sector in a pie graph is 12 cm^2, radius is 4cm, what is the angle?

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Answer 1 · 2015-07-12T01:20:53

$1.5$ $1.5$ (rad) $\approx 85.94$ $~~85.94$ degrees

Explanation:

Radius of Circle = 4cm

Recall : Area of disk = $π \cdot r^{2}$ $pi*r^2$

Here, the area of our graph = $π \cdot 4^{2} = 16 \cdot π$ $pi*4^2 = 16*pi$ cm²

Then our sector of $12$ $12$ cm² is representing $\frac{12}{16 \cdot π}$ $12/(16*pi)$ of the pie graph.
And $\frac{12}{16 \cdot π} = \frac{3}{4 \cdot π} \approx 0.2387 \approx 23.87 %$ $12/(16*pi)=3/(4*pi)~~0.2387~~23.87%$

Therefore, the $12$ $12$ cm² sector represents exactly $\frac{0.75}{π}$ $0.75/pi$ of the pie graph.

(It represents approximately $23.87 %$ $23.87%$ of pie chart.)

Now we want the angle of the sector (in radian measure)
If the sector cover $100 %$ $100%$ of the graph, then we have the angle measure is equal to $2 π$ $2pi$

Thus :
$1 \Leftrightarrow 2 π$ $1 <=> 2pi$ (rad)
$0.75 \Leftrightarrow 1.5 π$ $0.75<=>1.5pi$ (rad)
$\frac{0.75}{π} \Leftrightarrow 1.5$ $0.75/pi<=>1.5$ (rad)

The angle measure of the sector is equal to $1.5$ $1.5$ rad.

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A sector in a pie graph is 12 cm^2, radius is 4cm, what is the angle?

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