Final answer:
The volume of the propane tank with a cylinder and two hemispheres is found by calculating the volume of both shapes and adding them together. After calculations, the correct total volume is 870.46 ft³.
Step-by-step explanation:
To calculate the volume of a propane tank that is shaped like a cylinder with a hemisphere on each end, the volume of both the cylinder and the two hemispheres must be summed. For the cylindrical part, the volume (V) is given by the formula V = πr²h, where r is the radius and h is the height of the cylinder. Since the diameter is given as 7 feet, the radius r is 3.5 feet. The height (h) of the cylinder is the total height minus the diameter of the two hemispheres (since the diameter equals the height of one hemisphere), which is 9 feet - 3.5 feet - 3.5 feet = 2 feet.
Thus, the volume of the cylindrical portion is:
V_cylinder = π × (3.5 ft)² × 2 ft
To calculate the volume of a hemisphere, the formula is ½ of the volume of a sphere, which is ½(¾πd³), where d is the diameter. Therefore, the volume of one hemisphere is:
V_hemisphere = ½(¾π×(7 ft)³)
Since there are two hemispheres, their total volume is:
V_total_hemispheres = 2 × V_hemisphere
Adding the volumes of the cylinder and the two hemispheres gives the total volume of the tank. After performing the calculations, the correct answer is option A) 870.46 ft³.