A hemispherical tank is filled with water and has a diameter of 19 feet. If water weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank, to the nearest pound?

Answer 1

The easiest way to approach this problem is to solve it as if the question were asking about a full sphere, then divide by 2 (since it is hemispherical).

The first step is to find the volume of the sphere. We can use the equation:

V_s = 4/3 * pi * r³

Where V_s is the volume of a sphere.

We can calculate the radius by dividing the diameter by 2: 19 ft/2 = 9.5 feet.

Thus, the volume is:

V_s = 4/3 * pi * r³

V_s = 4/3 * pi * (9.5)³

V_s = 3591.364 ft³

Since the tank is hemispherical, rather than spherical, we divide this volume by 2 to find the volume of the hemisphere:

V_h = V_s/2 where V_h is the volume of the hemisphere and V_s is the volume of the sphere

V_h = 3591.364 ft³/2 = 1795.682 ft³

Now, we multiply the volume by the density of the water to find the total weight of the water in the full tank:

62.4 pounds/ft³ * 1795.682 ft³ = 112050.5569 pounds

The cubic feet cancel, leaving us with just pounds.

The final answer is thus 112050.5569 pounds, or, rounded to the hundredths place, 112050.56 pounds.