Answer:
3 cones are required to fill the cylinder.
Vcyl =
and Vcone = ![\frac{1}{3} \pi r^2 h](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20r%5E2%20h)
The volume of cylinder is 3 times the volume of cone having same base and height.
Step-by-step explanation:
Consider the provided information.
Now we need to find the number cones to fill the cylinder.
The volume of a cone is:
![\frac{1}{3} \pi r^2 h](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20r%5E2%20h)
The volume of cylinder is:
![\pi r^2 h](https://tex.z-dn.net/?f=%20%5Cpi%20r%5E2%20h)
To find the the number cones to fill the cylinder simply divide the volume of cylinder by volume of cone as shown:
![\frac{\pi r^2 h}{\frac{1}{3} \pi r^2 h}=3](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi%20r%5E2%20h%7D%7B%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20r%5E2%20h%7D%3D3)
Hence 3 cones are required to fill the cylinder.
The formula for the volume of each shape is:
Vcyl =
and Vcone = ![\frac{1}{3} \pi r^2 h](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20r%5E2%20h)
The relationship between the volume of the cylinder and the volume of the cone is: The volume of the cone is 1/3 of a cylinder that has the same base and height or the volume of cylinder is 3 times the volume of cone having same base and height.