A storage bin has the shape of a cylinder with a conical top. What is the volume of the storage bin if its radius is r = 4.5 ft, the height of the cylindrical portion is h =7.6 ft, and the overall height is H = 15.1 ft? Round to the nearest tenth.
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A storage bin has the shape of a cylinder with a conical top. What is the volume of the storage bin if its radius is {eq}r = 4.5 ft {/eq}, the height of the cylindrical portion is {eq}h =7.6 ft {/eq}, and the overall height is {eq}H = 15.1 ft {/eq}? Round to the nearest tenth.
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Janis April 18, 2023 в 02:26The volume of the storage bin can be found by adding the volume of the cylindrical portion and the conical portion. The volume of the cylindrical portion is: {eq}V_{cylinder}=pi r^2h {/eq} Substituting the given values: {eq}V_{cylinder}=pi(4.5)^2(7.6)approx 610.8 ft^3 {/eq} The volume of the conical portion is: {eq}V_{cone}=dfrac{1}{3}pi r^2H {/eq} Substituting the given values: {eq}V_{cone}=dfrac{1}{3}pi(4.5)^2(15.1-7.6)approx 318.5 ft^3 {/eq} Therefore, the total volume of the storage bin is: {eq}V_{tot} = V_{cylinder} + V_{cone} \approx 929.3 ft^3 {/eq} Rounding to the nearest tenth, the answer is: {eq}boxed{929.3} ft^3 {/eq}.
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