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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?

Ask by Curry Welch. in the United States
Mar 06,2025

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The total weight of the liquid in the tank is approximately 129,474 pounds.

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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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