A cylinder with a radius of 4 centimeters and a height of 9 centimeters has the same volume as a cone with a radius of 3 centimeters.
What is the height of the cone?
Answer options with 4 options
A.
12 centimeters
B.
16 centimeters
C.
36 centimeters
D.
48 centimeters
A. 12 centimeters
To find the height of the cone, we first need to find the volume of the cylinder and then set it equal to the volume of the cone:
Volume of cylinder = πr^2h
Volume of cone = (1/3)πr^2h
For the cylinder:
Volume = π(4^2)(9) = 144π cm^3
For the cone:
144π = (1/3)π(3^2)h
144π = 3πh
48 = h
Therefore, the height of the cone is 12 centimeters, which corresponds to option A.