The radius of the barrel, r = 3 feet. Suppose the cylindrical part of the barrel has a height of h feet.
Then volume of cylindrical part = pi*r2*h cu ft
and volume of hemisphere = 2/3*pi*r3 cu ft
So total volume = pi*r2*(h + 2r/3) = 868.87
that is, pi*9*(h + 2) = 868.87
h + 2 = 30.73 so that h = 28.73
Therefore, the total height of the barrel, including the hemispheric top is
28.73 + 3 = 31.73 feet.
More a silo than a barrel, but that's another matter.
The radius of the barrel, r = 3 feet. Suppose the cylindrical part of the barrel has a height of h feet.
Then volume of cylindrical part = pi*r2*h cu ft
and volume of hemisphere = 2/3*pi*r3 cu ft
So total volume = pi*r2*(h + 2r/3) = 868.87
that is, pi*9*(h + 2) = 868.87
h + 2 = 30.73 so that h = 28.73
Therefore, the total height of the barrel, including the hemispheric top is
28.73 + 3 = 31.73 feet.
More a silo than a barrel, but that's another matter.
The radius of the barrel, r = 3 feet. Suppose the cylindrical part of the barrel has a height of h feet.
Then volume of cylindrical part = pi*r2*h cu ft
and volume of hemisphere = 2/3*pi*r3 cu ft
So total volume = pi*r2*(h + 2r/3) = 868.87
that is, pi*9*(h + 2) = 868.87
h + 2 = 30.73 so that h = 28.73
Therefore, the total height of the barrel, including the hemispheric top is
28.73 + 3 = 31.73 feet.
More a silo than a barrel, but that's another matter.
The radius of the barrel, r = 3 feet. Suppose the cylindrical part of the barrel has a height of h feet.
Then volume of cylindrical part = pi*r2*h cu ft
and volume of hemisphere = 2/3*pi*r3 cu ft
So total volume = pi*r2*(h + 2r/3) = 868.87
that is, pi*9*(h + 2) = 868.87
h + 2 = 30.73 so that h = 28.73
Therefore, the total height of the barrel, including the hemispheric top is
28.73 + 3 = 31.73 feet.
More a silo than a barrel, but that's another matter.
The radius of the barrel, r = 3 feet. Suppose the cylindrical part of the barrel has a height of h feet.
Then volume of cylindrical part = pi*r2*h cu ft
and volume of hemisphere = 2/3*pi*r3 cu ft
So total volume = pi*r2*(h + 2r/3) = 868.87
that is, pi*9*(h + 2) = 868.87
h + 2 = 30.73 so that h = 28.73
Therefore, the total height of the barrel, including the hemispheric top is
28.73 + 3 = 31.73 feet.
More a silo than a barrel, but that's another matter.