Answer:
- The ratio of the height of the cone to the height of the cylinder is 3:1
- The ratio of the height of the cone to radius of the sphere is 4:1
Step-by-step explanation:
Note that the radii of all the structures are the same.
Let the height of the cone be H and the height of the cylinder be h
The volume of each of the shapes are given below as
Volume of cylinder = πr²h
Volume of a cone = (1/3)πr²H
Volume of a sphere = (4/3)πr³
1) The ratio of the height of the cone to the height of the cylinder
To obtain this, we equate the volume of those two structures
Volume of the cone = Volume of the cylinder
(1/3)πr²H = πr²h
πr² cancels out on both sides and we're left with
(H/3) = h
H = 3h
(H/h) = (3/1)
So, The ratio of the height of the cone to the height of the cylinder is 3:1
2) The ratio of the height of the cone to radius of the sphere
Similarly equating the volumes of the cone and the sphere
(1/3)πr²H = (4/3)πr³
(1/3)πr² cancels out on both sides and we're left with
H = 4r
(H/r) = (4/1)
The ratio of the height of the cone to radius of the sphere is 4:1
Hope this Helps!!!
