Answer:
16 * (cube root of 0.5)
Explanation:
Radius of the big cone = 12 cm / 2 = 6 cm
Let r = radius of the small cone (cone of water), and h = the height of the small cone
Also, r / h = 6 / 16, so that h = (16/6)r = (8/3)r.
Thus, since the volume of the big cone = (1/3)π(r^2*h)=(1/3)π(6^2*16), and the volume of the small cone = (1/3)π(r^2*h)=(1/3)π(r^2*(8/3)r) = (1/3)π(r^3*(8/3)), and the volume of the small cone is half the volume of the big cone, we have that
(1/3)π(r^3*(8/3))=(1/2)((1/3)π(6^2*16))
(r^3*(8/3))=(1/2)((6^2*16))
r^3 = (3/8)(1/2)(6^2)(16)
r^3 = (1/2)(6^3)
r = (cube root of 1/2)(6),
and
h = (8/3)r = (8/3)(cube root of 1/2)(6) = 16(cube root of 1/2), the depth of the water.