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avatar+1679 

A cone has a volume of $36\pi\text{ cm}^3$ and a height of $3$ cm.  A cylinder has a radius equal to one-third the radius of the cone, and a height equal to four times the height of the cone.  What is the positive difference between the volume of the volume of the cone and the volume of the cylinder?  Express your answer in terms of $\pi$.

 Aug 25, 2023
 #1
avatar+128732 
+1

Volume of cone =  (1/3) pi  r^2 * h

36 pi  = (1/3) pi * r^2 * 3      divide out pi  and simplify

36 = r^2

r = 6

 

Volume of the  cylinder =  pi * ( (1/3) * 6)^2 * (3 * 4)  =  pi ( 2)^2 * 12 =  48pi

 

Positive difference  between volumes =  48 pi  - 36pi  =   12 pi

 

 

cool cool cool

 Aug 25, 2023

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