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 13
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 approximately 3.14.
Since the cone is half full of water, we know that the volume of the water is half of the volume of the cone. Let's call the volume of the cone Vc and the volume of the water Vw. Then we have:
Vw = (1/2)Vc
We can also use the fact that the diameter of the cone is 13 to find the radius, which is half the diameter:
r = 13/2 = 6.5
Now we can plug in the values we know and solve for the height of the water, hw:
Vc = (1/3)πr^2h
Vw = (1/2)Vc = (1/2)(1/3)πr^2h
Simplifying, we get:
Vw = (1/6)πr^2h
(1/6)πr^2h = (1/2)(1/3)πr^2h
(1/6)h = (1/6)
h = 1
Therefore, the height of the water in the cone is 1 unit when the height of the cone is 16 and the diameter is 13.
AAAaannndd the bot gets it wrong yet again!
v = 1/12 π d^2 h
since r = 13/16 h,
we want h when
π/12 (13/16)^2 h^3 = 1/2 π/6 * 13^2 * 16
h = 8∛2