The volume of a cylinder is represented below
V=27π cm3
What would be the volume of a cone that has the same height and diameter as the cylinder?
(1 point)
Responses
V=81π cm3
V=81π cm3
V=3π cm3
V=3π cm3
V=9π cm3
V=9π cm3
V=18π cm3
V=18π cm3
The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius and h is the height.
In this case, since the cone has the same height and diameter as the cylinder, the radius of the cone would be half of the diameter.
Given that V = 27π cm3 for the cylinder, we can find the diameter using the formula V = πr²h and solve for r.
27π = πr²h
27 = r²h
Since the radius of the cylinder is half of the diameter, the diameter would be d = 2r.
Using the formula d = 2r, we can solve for r:
d = 2r
2r = 27
r = 27/2 = 13.5
Now, we can calculate the volume of the cone using the formula V = (1/3)πr²h with the radius we found:
V = (1/3)π(13.5)²h = (1/3)π(182.25)h
Since the height of the cone is the same as the cylinder, the volume of the cone would be:
V = (1/3)π(182.25)(h) = (1/3)(27π)(h) = 9π(h) = 9π cm3
Therefore, the correct response is:
V = 9π cm3