A hemispherical tank is filled with water and has a diameter of 12 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?

28229

V=

\,\,\frac{4}{3}\pi r^3
3
4

πr
3

Volume of a Sphere
V=
V=
\,\,\frac{1}{2}\left (\frac{4}{3}\pi r^3 \right)
2
1

(
3
4

πr
3
)
Volume of a Hemisphere
V=
V=
\,\,\frac{1}{2}\left (\frac{4}{3}\pi (6)^3 \right)
2
1

(
3
4

π(6)
3
)
If diameter is 12, then radius is 6.
V=
V=
\,\,452.3893\text{ }\text{ft}^3
452.3893 ft
3

452.3893\text{ }\text{ft}^3 \cdot\frac{62.4\text{ }\text{lbs}}{\text{ft}^3}=28229\text{ }\text{lbs}
452.3893 ft
3

ft
3

62.4 lbs

=28229 lbs

To find the total weight of the water in a full tank, we need to calculate the volume of water in the tank and then multiply it by the weight of water per cubic foot.

1. First, let's find the volume of the water in the tank. Since the tank is hemispherical, the volume of water will be half of the volume of the entire sphere.

2. The formula to calculate the volume of a sphere is V = (4/3)πr³, where V is the volume and r is the radius. In this case, the diameter of the tank is given as 12 feet, so the radius (r) is half of the diameter, which is 6 feet.

3. Plugging the values into the formula, we get V = (4/3)π(6³) = (4/3)π(216) = 288π cubic feet.

4. Now, we can calculate the weight of the water by multiplying the volume by the weight of water per cubic foot. Given that water weighs 62.4 pounds per cubic foot, we have:

Weight = (Volume of water) * (Weight per cubic foot) = 288π * 62.4 ≈ 1807.44π pounds.

5. To get the weight to the nearest pound, we need to approximate the value of π. Let's take π as 3.14:

Weight ≈ 1807.44 * 3.14 ≈ 5687.93 pounds.

Therefore, the total weight of the water in a full tank is approximately 5687 pounds.

v = 4/3 π r^3 = 4/3 * π * 196

weight = v * 62.4 ... lbs