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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.

 Feb 11, 2024
 #1
avatar+129852 
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The radius of the circle can be  found as

 

25 pi = pi *r^2

25 = r^2

r = 5

 

Ler R be the radius of the sphere

 

R^2 =   [ 5^2 + r^2 ] =  [ 5^2 + 5^2 ]  =  50

 

Surface area of sphere  =

 

4 pi R^2  = 

 

4 pi * 50  =

 

200 pi

 

 

cool cool cool

 Feb 11, 2024
edited by CPhill  May 30, 2024

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