Question

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.

Answer 1

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.