A cylinder has a radius of 5 cm and a height of 12 cm. What would the might of a cone need to be if it has the sane volume and radius? Round to the nearest cm.
if you type in your question on google it will pull up some videos and other stuff right away, but i think the first video you see will be able to help you out
cylinder: pi r^2 h
cone: 1/3 pi r^2 h
if the volumes and radii are the same, then the cone would have to be 3 times as tall.
pi*r^2*12 = pi*r^2*h/3.
Divide both sides by pi*r^2:
12 = h/3,
h = ---------cm. = Ht. of cone.
To find the height of the cone, we need to set the volumes of the cylinder and the cone equal to each other because they have the same radius.
The volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.
The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
Given that the radius of the cylinder is 5 cm and the height is 12 cm, we can find the volume of the cylinder as follows:
V_cylinder = π(5^2)(12)
V_cylinder = 300π cm^3
Now, we need to set this volume equal to the volume of the cone and solve for the height of the cone.
300π = (1/3)π(5^2)h_cone
300 = (1/3)(25)h_cone
900 = 25h_cone
h_cone = 36 cm
Therefore, the height of the cone needs to be approximately 36 cm in order to have the same volume and radius as the given cylinder.