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Hai thereee!!! I've been putting off this question for a long time and have been doing other problems... so now i need a bit of help on this ;-;

 

sorry for the trouble:

 

The volume of a cylinder is $54\pi$ $\text{cm}^3$. How many cubic centimeters are in the volume of a cone with the same radius and height as the cylinder? Express your answer in terms of $\pi$.

 

thank you so much for the help!!! :D

 Jul 28, 2021
 #1
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Volume of cylinder = pi 2r h = 54pi

                                  rh = 54/2 = 27

                                    h = 27/r

 

volume of cone = 1/3 pi r^2 h

                              1/3 pi r^2 27/r = 9 pi r          do you have the radius ?

 Jul 28, 2021
 #4
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I think we don't need the radius, EP.  The problem asks for the solution in terms of pi.  I got 18π as shown below.    

Guest Jul 28, 2021
 #5
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You are right...I was using the SURFACE AREA of a cylinder.....   Mistake !   D'Oh!

Thanx !   ~EP

ElectricPavlov  Jul 28, 2021
 #2
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no radius was provided, no

 Jul 28, 2021
 #3
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Compare the formulae for the volume of a cylinder and of a cone.  

 

Volume of a cylinder is        π • r2 • h  

 

Volume of a cone is     1/3 • π • r2 • h   

 

A cone has 1/3 the volume of a cylinder that has the same base and same height.  

 

So the cone in the question has a volume of 1/3 • 54π cm3  or  18π cm3  

 Jul 28, 2021
 #6
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thank you so much! I really appreciate it! ^^

 Jul 28, 2021

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