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The base of a square pyramid is inscribed within the base of a cone, and both solids have the same vertex. The volume of the cone is 200 in.3. What is the volume of the square pyramid, to the nearest tenth of a cubic inch?

 May 19, 2020
 #1
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Vcone  =   (1/3) pi r^2 *  h

 

So.....we have

 

200  = (1/3)pi r^2  * h       multiply  both sides by 3

 

600 =pi r^2  *  h          solve for  h

 

600 /[ pi r^2 ] =  h  =  height of pyramid and cone

 

The  volume  of  the  pyramid  =  (1/3)  side ^2 * h

 

The  base  of the pyramid  will  be a square inscribed on  the crcular base  of the cone

The  radius of the cone  = r    and the diameter  =  2r

So.....the side  of the  pyramid  =  2r/√2  =  √2 * r

 

So.......the  volume  of  the  pyramid  =

 

(1/3) ( side)^2  * height

 

(1/3) (√2 * r)^2  *   ( 600 /[pi r^2] )  =

 

(1/3) ( 2r^2) * 600  /[ pi r^2 ] =

 

(1/3)  (2  * 600)  / pi   =

 

400/ pi in^3   ≈  127.3 in^3

 

 

cool cool cool

 May 19, 2020

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