A tank in the shape of a hemisphere has a diameter of 18 feet. If the liquid that fills the tank has a density of 84.8 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
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To find the total weight of the liquid in the tank, we first calculate the volume of the hemisphere using the formula \( V = \frac{2}{3} \pi r^3 \). The radius \( r \) of the tank is half the diameter, so \( r = 9 \) feet. The volume is \( V = \frac{2}{3} \pi (9)^3 \approx 523.6 \) cubic feet. Now, we multiply the volume by the density of the liquid: Total weight = Volume × Density = \( 523.6 \, \text{ft}^3 \times 84.8 \, \text{lb/ft}^3 \approx 44358 \) pounds. So, rounding to the nearest full pound, the total weight of the liquid in the tank is approximately **44,358 pounds**.
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