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

Guest Jul 28, 2021

#1**+1 **

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 ?

ElectricPavlov Jul 28, 2021

#4**0 **

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**0 **

You are right...I was using the SURFACE AREA of a cylinder..... Mistake ! D'Oh!

Thanx ! ~EP

ElectricPavlov
Jul 28, 2021

#3**+1 **

Compare the formulae for the volume of a cylinder and of a cone.

Volume of a cylinder is π • r^{2} • h

Volume of a cone is 1/3 • π • r^{2} • 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 cm^{3} or **18π cm ^{3}**

Guest Jul 28, 2021