Final answer:
The volume of the cylinder is calculated by first deriving the radius from the given information and then applying it to the formula for the volume of a cylinder (V = πr²h). The radius is found to be 7m, which gives a cylinder volume of 1617 m³.
Step-by-step explanation:
The subject of this question is mathematics, specifically in the domain of geometry and volumetric calculations. We are given the height (h) of a right circular cylinder and asked to find its volume. We need to solve for the radius (r). The first step is to formulate an equation using the given information. We know the area of the circular face of a cylinder is given by πr² and the area of the curved surface is given by 2πrh.
According to the problem, three times the sum of the areas of the circular faces (which would be 2*πr²) equals twice the area of the curved surface (which would be 2*2πrh), that is, 3*2*πr² = 2*2πrh. Solving this equation for r, we get r = 7m.
Once we have the radius, we can calculate the volume of the cylinder using the formula V = πr²h. Substituting r = 7m and h = 10.5m, we get V = π*7²*10.5 = 1617 m³.
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