**Hydrostatic Force on a Submerged Circular Plate**A circular plate with a radius of 9 meters is submerged vertically in water as illustrated in the diagram below. We are required to express the hydrostatic force against one side of the plate as an integral and evaluate it. Your answer should be rounded to the nearest whole number. Use 9.8 m/s² for the acceleration due to gravity. Recall that the mass density of water is 1000 kg/m³.### Integral ExpressionThe hydrostatic force \( F \) can be expressed as:\[F = \rho g \int_{-9}^{0} (12 - y) \sqrt{81 - y^2} \, dy\]Where:- \(\rho\) is the mass density of water, \(1000 \, \text{kg/m}^3\).- \(g\) is the acceleration due to gravity, \(9.8 \, \text{m/s}^2\).- \( (12 - y) \) represents the depth of the submerged section.- \( \sqrt{81 - y^2} \) is derived from the circle's equation for the half-chord length at depth \( y \).### CalculationEvaluating the integral gives the hydrostatic force:\[F \approx 14,962,777 \, \text{N}\]### Diagram DescriptionThe diagram shows a circle submerged in water. The radius of the circle is 9 meters, and it is vertically positioned with a center depth of 12 meters from the surface. A vertical line through the center is annotated, extending 3 meters above the top of the circle to indicate the depth from the water's surface.This setup helps visualize the distribution of pressure across the submerged plate, informing calculations for hydrostatic force.

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