Answer:
height is = 3/2 ft
Explanation:
a cones volume can be represented by 1/3(h)(pi)(r^2)
we must go backwards to find this question out
if the diameter is 2/3 then the radius is 1/3
then you must square that
that is 1/3 * 1/3 which is 1/9
1/9(1/3)(pi)(h) is 1/18(pi)
we can remove pi from both sides and multiply the 1/9 and the 1/3
1/27(h) = 1/18
we must find the lcm or least common multiple to figure this out
the lcm is 54
1/27 is essentially 2/54 and 1/18 is 3/54
2/54(h) = 3/54
we can multiply each side by 54
2h = 3
divide 2 on both sides
h is 3/2