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An air duct in a stadium has a circular cross section with a radius of 15 inches and a length of 49 feet and is open at both ends. What is the volume of the​ duct, and how much paint​ (in square​ feet) is needed to paint the exterior of the​ duct?

Respuesta :

Answer:

240.56 ft³,384.895 ft²

Step-by-step explanation:

15 inches = 1.25 feet where 1 inch = 0.0833 feet

volume of the air duct = volume of a cylinder = πr²h

volume of the air duct = 3.142 × ( 1.25 ft)² × 49 ft = 240.56 ft³

the exterior of the duct = curved surface area of a cylinder = 2πrh = 2 × 3.142 × 1.25 ft × 49 ft = 384.895 ft²

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