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The cross section at this point forms a circle and its area is pi/32 which equals 9*pi square units.

* * * * *

Not quite.

If the radius of the sphere is R units then the radius of the cross section is sqrt(R2 - 32)

Therefore the cross sectional area is pi*(R2 - 32) square units.

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Q: What is the area of the cross section of a sphere that is 3 units from the center of the sphere?
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What is the radius of a cross section of a sphere that is 3 units from the center of the sphere?

If the radius of the sphere is R units then the radius of the cross section is sqrt(R2 - 32) Therefore the cross sectional area is pi*(R2 - 32) square units.


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