A cone is exactly half full of water by volume. How deep is the water in the cone when the height of the cone is 16 and the diameter is 12
We can start by using the formula for the volume of a cone, which is:
V = (1/3)πr^2h
where V is the volume, r is the radius, h is the height, and π is pi (approximately 3.14).
We know that the cone is half full of water, so the volume of water is half the volume of the cone. Let's call the volume of the cone Vc and the volume of water Vw:
Vw = (1/2)Vc
We can also use the fact that the diameter of the cone is 12 to find the radius:
r = d/2 = 12/2 = 6
Now we can substitute these values into the formula for the volume of the cone:
Vc = (1/3)πr^2h
Vc = (1/3)π(6^2)(16)
Vc = 603.19
And we can use the equation for the volume of water to find Vw:
Vw = (1/2)Vc
Vw = (1/2)(603.19)
Vw = 301.59
Finally, we can use the formula for the volume of a cone to find the height of the water:
Vw = (1/3)πr^2h
301.59 = (1/3)π(6^2)h
301.59 = 113.1h
h = 2.67
Therefore, the water in the cone is approximately 2.67 units deep.