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
+36916 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 ?
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.
+36916 You are right...I was using the SURFACE AREA of a cylinder..... Mistake ! D'Oh!
Thanx ! ~EP
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
