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A plane and a sphere intersect in a circle. The circle has an area of $25 \pi$. The distance between the plane and the center of the sphere is $5$ units. Find the surface area of the sphere.

 Jul 20, 2024
 #1
avatar+1950 
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First, let's find the radius of the circle. We simply have

25π=πr225=r2r=5

 

Let's let R be the radius of the sphere. 

R2=[52+r2]=[52+52]=50

 

Now, we can calculate the surface area of the sphere. We have

4πR2=4π50=200π

 

So, the answer is 200π

 

Thanks! :)

 Jul 21, 2024
edited by NotThatSmart  Jul 21, 2024

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