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The two bases of a cylinder are two parallel cross sections of a sphere. We know the radius of the sphere is 3 and the height of the cylinder is 4 Find the volume of the cylinder.

[asy] size(4cm); import three; currentprojection=orthographic(0,2,0.2); triple A,B,C,D,P,Q; A=(0.8,0,0.6); B=(0,0.8,0.6); C=(-0.8,0,0.6); D=(0,-0.8,0.6); P=(0,0,1); Q=-P; draw(A..B..C); draw(C..D..A,dashed); A=(0.8,0,-0.6); B=(0,0.8,-0.6); C=(-0.8,0,-0.6); D=(0,-0.8,-0.6); draw(A..B..C); draw(C..D..A,dashed); draw(A--A+(0,0,1.2)); draw(C--C+(0,0,1.2)); A=(1,0,0); C=(-1,0,0); draw(A..P..C..Q..A); dot(origin); [/asy]

 

(sorry idk how to put the picture)

 
 4 hours ago
 #1
avatar+130116 
+1

 

 

 

We can represent the cross-section pf the sphere as a circle with the equation

x^2 + y^2  = 9

 

Let  1/2 the height of the cylinder = 2  =  BG

 

So...

 

x^2 + 2^2   = 9

 

x^2    =  5

 

x = sqrt 5  =  the radius of the cylinder   = AG   

 

Cylinder volume  = pi * (sqrt 5)^2 * 4   = pi * 5 * 4  =    20  pi

 

cool cool cool

 2 hours ago

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