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.
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
1 answer