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Volume again. Sorry, I have over 50 questions and I have a hard time with volume...

Guest Nov 12, 2018
 #1
avatar+92608 
+1

First one

 

We need to find the height of the pyramid

 

Cone volume  =  (1/3) (3.14)  * ( radius of cone )^2 * ( height of cone )

 

1884  =  (1/3) (3.14) * (10)^2 * (height of cone)

 

1884 = (100/ 3)) (3.14) * height of cone   

 

Divide both sides by  (100/3) (3.14)

 

Height of cone  =  1884 /   [ (100/3) (3.14)]  =  18  =  height of pyramid

 

 

Volume of (square ) pyramid  =   (1/3)  [ side of base ]^2 * 18  =

 

(1/3)* ( 20^2] * 18  =  2400 in^3

 

So....the difference is    2400 - 1884  =     516 in^3

 

 

cool cool cool

CPhill  Nov 12, 2018
 #2
avatar+92608 
+1

Second.....easier than the first one   !!!

 

Volume of cone  = (1/3)  3.14  * ( radius of cone)^2 * height of cone  =

 

(1/3) (3.14) * (2^2) * 6  =     25.12   (1)

 

Volume of cylinder  = pi * radius^2 * height  =

 

pi * 2^2 * 12  =      150.72     (2)

 

 

So....total volume is    (1) + (2)  =  175.84  in^3

 

 

cool cool cool

CPhill  Nov 12, 2018
 #3
avatar+92608 
+1

Last one.....a little more conceptual

 

Radius of cylinder and hemisphere = r

 

Height of cylinder  =   h - r

Height of hemisphere = r

 

Total  volume of cylinder  =   pi  [ r^2]  * [ h - r ]

 

Total volume of hemisphere  = pi  (4/3) (r^2) * (r)  * (1/2)  =  (2/3) pi r^3 = pi ( 2/3) r^3

 

(2/3) pi r^3  + pi r^2 ( h - r )   ⇒  "C"

 

 

cool cool cool

CPhill  Nov 12, 2018

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