For the partial Wheel of Emotions below, determine the area of each petal’s sector of the inner circle, if the radius of the entire circle is 6 cm and the area of the ring is identical to the area of the inner circle.

For the partial Wheel of Emotions below determine the area of each petals sector of the inner circle if the radius of the entire circle is 6 cm and the area of class=

Respuesta :

Okay, here we have this:

Considering the provided figure, we are going to calculate the requested area, so we obtain the following:

So from the given information we have:

Area of the wheel = Area of the inner circle + Area of the ring

And since the area of the inner circle and the ring are equal, we have:

Area of the wheel = Area of the inner circle + Area of the inner circle

Area of the wheel = 2*Area of the inner circle

Remember that the area of a circle is:

Area of the wheel = π r^2

So substituting:

2*Area of the inner circle=π r^2

Area of the inner circle=(π r^2)/2

And the area of each petal of the inner circle is:

Area of each petal’s sector of the inner circle=Area of the inner circle / number of petals

Area of each petal’s sector of the inner circle=((π r^2)/2) / number of petals

Area of each petal’s sector of the inner circle=((π r^2)/2) / 8

So finally replacing with the given information:

Area of each petal’s sector of the inner circle=((π* (6cm)^2)/2) / 8

Area of each petal’s sector of the inner circle=((π* 36cm^2)/2) / 8

Area of each petal’s sector of the inner circle=((36π cm^2)/2) / 8

Area of each petal’s sector of the inner circle=(18π cm^2) / 8

Area of each petal’s sector of the inner circle=18π/8 cm^2

Area of each petal’s sector of the inner circle=2.25π cm^2

Finally we obtain that the Area of each petal’s sector of the inner circle is 2.25π cm^2.

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